Papers

To solve a family of large linear systems where the system matrix depends on the family parameter quadratically, we propose a new solution approach. Our method employs the derivatives of solutions with respect to the parameter. It turns out that the accumulated solution derivatives of increasing order, evaluated at a single specially chosen parameter value, provide successively better approximations to solution subspaces for the whole linear system family. We show that the derivatives can be computed by a recurrence, involving, at each step, solving a linear system with the same matrix. Constructing an orthonormal basis for the subspace spanned by the derivatives then leads to an efficient solver where just a single (sparse) LU factorization (or a single preconditioner setup in an iterative scheme) suffices to solve the whole linear system family. We call the new method ODB (orthonormal derivative basis method). As shown in numerical tests, compared to conventional solution methods, the ODB method allows to drastically reduce computational costs.

Implicit time integration is the standard way to overcome the tight CFL time step restriction when solving nonstationary PDEs numerically. However, within an adaptive time accurate integration, the time step size selection is governed not only by stability but also by accuracy requirements. Therefore, an eligible question to ask is: is (unconditionally) stable implicit time stepping really needed if the time step is restricted by accuracy considerations anyway? And how much do we then lose (in terms of the time step size) when switching from the expensive implicit time stepping to stabilized explicit schemes? An answer to this question is also important because such a switch is often done when solving large scale nonstationary PDEs on massively parallel computers. This paper attempts to answer these questions by numerical tests for two particular adaptive time accurate settings: (i)~nonstationary convection-diffusion equations and (ii)~nonlinear heat equations.

Assembly modeling plays an important role in constructing product models, yet it is still mainly performed via interactive operations that are experience-dependent and labor-intensive. Data-driven strategies hold promise for automating this process; however, existing approaches either predict poses that cannot directly generate editable B-Rep assembly constraints or require prescribed part pairs or predefined assembly faces. To reduce the large candidate space of constraint prediction without predefined assembly faces, we propose a data-driven framework based on assembly feature mate prediction. The framework performs automatic assembly modeling from unassembled B-Rep parts, using assembly features to group the geometric entities of local mating interfaces and restrict candidate formation. Given the lack of suitable assembly feature annotations in existing datasets, we construct a large-scale dataset through an automatic annotation pipeline. Using the annotated dataset, we train an attention-based network to predict assembly feature mates, with Engineering Compatibility Fusion (ECF) incorporating explicit engineering compatibility into learned matching scores. To improve the accuracy of automatic assembly modeling, we use assembly feature patterns (AFPs) to guide the matching process. Finally, a post-processing search selects assembly feature mate and AFP mate candidates, whose associated constraints are generated and solved to complete assembly modeling. Experimental results show that the framework achieves assembly constraint accuracies of 74.79% on the six-assembly comparison set and 64.09% on the extended test set of 16 assemblies, which includes the comparison set. With ground-truth face labels supplied as additional input, the corresponding accuracies increase to 81.78% and 80.93%, respectively.

Computational coarse-graining aims to replace a sequence of updates with a cheaper module while preserving task performance. We present a continuation-relative evaluation framework that assesses replacements through the computation that follows them, using downstream task quality and total execution cost as joint criteria. The framework distinguishes boundary representations, summaries of skipped computation, executed operations, and downstream loss. It makes interfaces and permitted deployment information explicit, combines fine-path references with directly trained controls using the same shortened architecture, and accounts for selection overhead. An exact loss decomposition separates replacement effects at a fixed downstream action from effects of changing that action. A finite construction shows how retained information can reduce the stipulated cost of zero-error prediction under fixed information and controller restrictions. Experiments in two frozen pretrained language models show that representation fidelity and task loss can favor different fitting objectives. In a prespecified comparison on a 1.7-billion-parameter model, next-token-loss training lowers in-distribution negative log-likelihood by 0.1901 nats per scored token compared with reconstructing the skipped blocks' output, using the same optimizer and update count. This ranking reverses in all nine paired comparisons under distribution shift. In a recursive expert prototype, the jointly adapted candidate lowers task error relative to frozen-bank and router-only baselines, but trails directly trained controls, and the tested input-only selectors fail the joint quality-cost criteria. Together, the protocol and studies provide explicit criteria and diagnostics for distinguishing useful computational replacement from local approximation gains within specified interfaces and evaluation settings.

Image-based crack analysis is essential for automated infrastructure inspection to reduce the cost, subjectivity, and safety risks of manual surveys. Despite advances in visual crack detection, methods that translate predictions into physically meaningful and engineering-interpretable crack condition information remain limited. To bridge this gap, this study proposes Inspect Any Crack (IAC), an innovative end-to-end crack recognition and condition assessment framework that automatically derives physical geometric measurements and continuous severity scores from concrete-crack imagery. At its core, IAC introduces SACv2-Tiny, an efficient crack segmentation model adapted from a vision foundation model. Trained on the challenging OmniCrack30K dataset, SACv2-Tiny achieved a $62.49\%$ F1-score and $45.45\%$ IoU on the test set and a mean zero-shot F1-score of $69.89\%$ across three unseen datasets, demonstrating robust segmentation that enables downstream analysis with limited post-processing. IAC further processes the predicted masks to quantify physical crack width and affected area using ground-sampling-distance calibration. Validation at 41 caliper-referenced locations yielded a mean relative width error of $7.33\%$. Beyond geometric quantification, IAC introduces a novel continuous crack-condition metric, the Crack Severity Index (CSI), bounded on $[0,100]$, which combines maximum crack width and affected-area ratio into a unified, standards-informed severity measure. Through these developments, IAC advances crack inspection beyond pixel-level recognition toward interpretable and automated infrastructure condition assessment.

We study investigative subgraph extraction for Anti-Money Laundering (AML) transaction graphs using the Shortest Paths Network Search Algorithm (SPNSA), which aggregates shortest paths among a small input feed of entities. Since SPNSA is highly sensitive to the feed choice, we evaluate several graph-only feed selection strategies and propose a motif-based coherent feed selection method. Experiments on the IBM-AML benchmark (HI-Small, LI-Small, HI-Medium) and the Elliptic Bitcoin transaction graph show that the proposed strategy yields markedly higher illicit ratios in the extracted subgraph than random and degree-based heuristics on Elliptic and the IBM-AML HI variants, while keeping the output compact.

Smart glasses are a promising platform for vision-language assistants, but private split inference remains expensive: protecting visual representations before transmission does not remove the cost of on-device vision encoding, wide protected tokens, or hardware-unaware execution. We present SAGE (Smart-glasses-Aware Guarded Encoding), a hardware-aware framework for efficient protected VLM inference on smart glasses. SAGE keeps raw images and unprotected visual tokens on the trusted device, reduces visual input cost, executes shape-specialized INT8 graphs, and compresses protected representations into compact 256-dimensional INT8 packets before transmission. Unlike efficiency methods optimized only for nominal model size, SAGE selects its operating point using downstream answer quality together with measured latency, memory, and thermal behavior on real Mentra Live glasses. On a matched Qwen workload, SAGE reduces glasses inference latency by 39.18%, device-sensor temperature rise by 21.91%, and protected packet size by 96.56%, while retaining 85.62% of the protected reference's relaxed utility and comparable prompted containment. Direct glasses-to-phone tests deliver all 192 packets and reduce median packet-plus-acknowledgment time from 71.3 to 10.0 ms. The compact protected interface also transfers across four additional VLM families. These results show that private wearable VLM inference must be optimized jointly across representation protection, communication, and real-device execution rather than through model compression alone.

Molecular machine learning evaluates out-of-distribution performance with structure disjoint splits, a construction rule fixed once at the scale its library happened to have: threshold a pairwise distance, then assign whole connected components to folds. For predicting structures from mass spectra, the field has converged on single-linkage clustering under the myopic Maximum Common Edge Subgraph (MCES) distance at a threshold of 10. This convention was set on 29,000 molecules but public libraries now hold 227,690 molecules. MCES is NP-hard per pair over a quadratically growing set, and so the criterion has never been evaluated at that scale. We propose an optimized version of this criterion, allowing for computationally feasible application on the public libraries: Admissible bounds and a union-find skip reduce $2.6 \times 10^{10}$ molecular pairs to only $1.15 \times 10^{7}$ integer programs, a $2{,}259\times$ saving, while provably producing the lossless partition. We find that at this scale the graph percolates. A single component holds $95.5\%$ of the library, capping any test set at $4.5\%$. What remains is not merely smaller, but systematically different: a held-out compound outweighs a training compound 88.1% of the time, because a fixed absolute budget is a tighter relative tolerance on a larger molecule. Large library benchmarks using this splitting rule naively therefore conflate structural novelty with extrapolation to larger, more complex chemistry.

Translating visual brain activity into natural language offers a powerful window into human cognition and neural semantic representation. Most prior brain-captioning approaches project fMRI signals into language space using paired supervision. However, the widely used Natural Scenes Dataset (NSD) was built based only on image-fMRI pairs, while existing methods rely on MS-COCO captions as indirect textual supervision. Critically, during fMRI acquisition, participants observe only cropped image regions, whereas the associated MS-COCO captions describe full scenes. This mismatch creates a fundamental gap between neural representations and textual supervision, introducing an inherent semantic loss in NSD-based brain captioning. To mitigate this limitation, we reformulate brain captioning as Neural-Grounded Visual Captioning, where language is generated directly from visually grounded neural evidence rather than text supervision. We propose MindVLM, a framework that maps fMRI signals into subject-aware visual tokens and leverages a frozen vision language model (VLM) to produce interpretable and personalized descriptions. Instead of point-wise regression, MindVLM focuses on extracting semantically relevant visual cues from neural activity, naturally accommodating partial observability and inter-subject variability. Extensive experiments on NSD show that MindVLM consistently improves caption quality across multiple VLM backbones, including LLaVA-v1.5, Qwen2.5-VL, and Gemma3, beyond intrinsic model priors. Despite requiring neither text supervision nor an LLM during training and operating under an image-grounded inference paradigm distinct from conventional captioning methods, MindVLM remains competitive with supervised approaches, suggesting that subject-specific neural grounding provides an efficient, scalable, and interpretable path toward faithful brain-to-language generation.

Physics foundation models are an increasingly popular approach for building versatile emulators for spatiotemporal systems. They require tokenisation layers that lift physical field data into a latent representation suitable for dynamic processing. A typical choice for this layer is a convolutional encoder, which lifts field information in a locality-aware way and can be trained very efficiently. However, this choice cannot be applied to a large class of scientific computing problems where data are represented on unstructured meshes, for example simulations on domains with curved boundaries. Such data typically require graph neural network architectures, which are more expensive to train and, in the form currently used, encode information differently from their CNN counterparts, thus limiting the portability of physics emulators between these data regimes. In this work we introduce Mesh-Native Convolution (MNC), a locality-aware tokenisation layer that encodes unstructured mesh-based data in a way that is analogous to CNNs. This approach leads to models that can be trained once on mesh data and then deployed to arbitrary unstructured meshes, even if these are irregular, with minimal retraining. We show that this tokenisation approach can be used to retrofit grid-pretrained foundation models efficiently on unstructured meshes and provide theoretical results to confirm the consistency of this approach with classical CNN encoders. We demonstrate the favourable performance of this retrofitting approach, which in many cases reaches acceptable accuracy even in zero-shot deployment, and outperforms existing baselines after only a few epochs of fine-tuning, thus providing an efficient bridge between the two data regimes.

When a trader executes a large order, the relevant question is not what will the price be? but what would the price have been had I not traded? Market impact is thus a causal quantity, yet classical models (Almgren–Chriss, propagators) regress price on flow, which is biased whenever informed flow moves prices through information as well as trading. We present a proof-of-concept Causal Market Simulator: a continuous-time causal prior-data fitted network (PFN) trained on a synthetic market prior in which a hidden informational flow confounds the flow–price relation by construction, with confounding strength an exact per-episode knob. On this prior, the naive estimator's bias follows a closed form we confirm empirically (up to 68% overestimation), while the PFN tracks the unbiased true-parameter oracle at high confounding. Its do-ablated twin, the same model with the intervention inputs removed, collapses onto the pre-window mean. Zero-shot, the model responds at the ground-truth scale to metaorders in an ABIDES limit-order book ($+0.38$ pre-onset standard deviations against seed-replay counterfactuals), and its intervention response replicates on about 2,300 detected flow bursts in BTC/ETH/SOL perpetuals and 3,800 on Nasdaq equities, evidence consistent with, though not proof of, causal transfer. Off-prior the response degrades gracefully, and split-conformal recalibration repairs interval calibration. Transfer hinges on encoding the metaorder as added flow rather than a clamped price level, not on more training. A recurrent state-space variant closes the remaining shape gap: its impact accrues over execution duration where the transformer's stays flat, raising the correlation with measured metaorder impact from $+0.68$ to between $+0.92$ and $+0.96$, at the cost of weaker on-prior deconfounding that traces to the training recipe rather than to recurrence.

Bifurcations are ubiquitous in physical systems, from structural buckling to fluid and climate dynamics, yet they remain largely unexplored in deep learning. At a symmetry-breaking bifurcation, a single input admits multiple equally valid solutions, violating the one-to-one assumption underlying most learned physical surrogates. We introduce Bi-FORK, a generative framework for learning these one-to-many solution maps in high-dimensional systems. Bi-FORK generates complete trajectories through latent flow matching, preserving space and time coherence, and uses repulsion-guided sampling to recover distinct solution branches in a single amortized pass. We evaluate Bi-FORK on buckling beams, mechanical metamaterials, and Allen-Cahn phase separation, spanning continuous, discrete, and field-valued bifurcations with discretizations up to 260,000 points. Bi-FORK recovers the multimodal solution structure while scaling several orders of magnitude beyond prior approaches, opening generative modeling to high-dimensional bifurcating physical systems.

Physics-informed neural solvers often struggle with multiscale behavior and sharp gradients due to the use of global approximation spaces and nonconvex training. We introduce AB-PIELM, an adaptive-basis physics-informed extreme learning machine that combines domain decomposition with joint optimisation of spatial and spectral hyperparameters while retaining deterministic normal-equation training. The method adapts both the number and placement of subdomains and the locality of radial basis functions, enabling problem-dependent allocation of representational capacity without modifying the underlying solver. Experiments on oscillatory function approximation and singularly perturbed advection-diffusion equations demonstrate accurate solutions across a wide range of stiffness regimes while using substantially fewer neurons than existing neural and PIELM-based approaches. The learned hyperparameters are interpretable, concentrating resolution near sharp gradients. The framework also supports inverse problems, successfully recovering diffusion coefficients from sparse noisy observations using Bayesian optimisation. These results indicate that adaptive-basis PIELM formulations provide an efficient and stable alternative to gradient-trained neural PDE solvers and naturally extend to broader classes of differential equations.

Thermodynamic cycles are the foundation of energy conversion across natural and engineered systems, transforming heat into useful work. However, these cycles traditionally operate between fixed thermal reservoirs, restricting them to specific locations and temperature differences. Here, we introduce autonomous thermodynamic cycles enabled by robotic mobility and sensing, allowing robots to perform thermodynamic cycles by accessing spatially varying temperature fields. We experimentally realize this concept using multistable gas-filled capsules that circulate within the system across a thermal gradient. Our model reveals that rapid transitions in the capsules' energy states allow the system to operate as a mobile heat engine that harvests and stores energy. By linking the capsule-scale internal energy dynamics to the robot's large-scale navigation strategy, we optimize locomotion paths that balance motion cost and energy harvesting. These findings demonstrate that thermodynamic cycles can emerge when autonomous systems navigate their environments, offering an artificial analog of organisms that forage for energy across spatial resources.

AutoCFD5 Case 2 compares the participants' CFD results with wind tunnel measurements of surface pressure, velocity profiles and force coefficients. To place each run on a diagram of error against computational cost, these quantities must be combined into one number. This note defines that number, the joint error. Following the practice of interlaboratory proficiency testing (ISO 13528), every deviation from the experiment is expressed in units of the spread of the participants' results at that point, estimated robustly with the standard's Algorithm A. The point-wise spreads are pooled into one scale per component, so that every measurement point carries equal weight within its component. The joint error is a fixed weighted sum of five component errors. The scales are computed once from all AutoCFD5 submissions received by 5 October 2026 and then frozen, so that scores are reproducible and comparable across workshops.

Multi-photon interference is the resource most native to photonic quantum machine learning, yet experiments on photonic reservoirs have reported advantages, null results, and train-only effects. These outcomes cannot be compared: each measures task-dependent accuracy on different tasks and platforms. Here we resolve the question task-independently through the kernel geometry of boson-sampling feature maps. Interference redistributes feature variance across roughly twice as many effective dimensions as distinguishable-particle statistics, generating a large geometric separation between the corresponding kernels. The separation grows superlinearly with indistinguishability, is linear in Hong–Ou–Mandel visibility at small visibility for two to four photons, and retains approximately 80% of its magnitude at the source quality of current quantum processors. Under experimental sampling budgets the separation is learnable on adversarially constructed tasks (accuracy advantage +0.22 plus or minus 0.05) and an order of magnitude smaller on natural tasks, gated by kernel–task alignment. The results reconcile the existing experimental record and supply a pre-experimental protocol: kernel geometry establishes that an interference-specific learning resource exists, and task alignment determines whether a given task can access it; both are computable before committing significant hardware resources.

Physics-based models connect scientific explanation with quantitative prediction. Constructing them requires selecting physical processes, defining states and governing equations, specifying couplings, and identifying parameters from experiments. Existing AI systems remain limited in making these model structure decisions autonomously. We introduce EvoSim, a self-evolving AI scientist for physical modeling. It uses experimental discrepancies to drive mechanism and equation revisions and held-out experimental data to test physical plausibility. Exploration traces make updates to knowledge, skills, and multi-agent orchestration. This co-evolution improves physics-based models and EvoSim's ability to select mechanisms, diagnose failures, and coordinate research. We evaluate EvoSim on two industrial battery modeling tasks. It predicts lithium-metal-plating onset from 25 to 45 degrees Celsius and 2 C to 6 C with a mean absolute error of 1.79% in state of charge. Dynamic voltage prediction under vehicle driving conditions achieves a root mean square error of 7.62 mV, surpassing the reported accuracy of models developed by human experts. Self-evolution reduces model and physics errors by approximately 36% relative to baseline, demonstrating improved scientific modeling capability. EvoSim turns experimental observations into validated models and cumulative research expertise.

AI services incur inference costs during execution, while revenue may arrive later. Changing API prices, limited upfront capital, and service failures can limit operators' ability to sustain or expand their services. Beyond reducing per-request costs, operators need to plan future spending, fund execution before revenue arrives, and obtain compensation for specified losses. This requires clear agreements across services with different pricing and execution conditions. These agreements must distinguish rights to consume services from rights to receive payments, define obligations under uncertain costs and income, and specify which failures qualify for compensation and how much can be paid. We present TokenBank, a financial infrastructure that represents these commitments through structured contracts. It supports service-consumption rights, agreements that settle API-price differences in cash (forwards), financing through limited rights to future service revenue, and protection claims for specified service failures. Contracts specify participants, covered services, validity, ownership, fulfillment conditions, and settlement rules. Evaluation combines replay of 899,441 API requests, real model-driven agent execution, and contract API tests. In a zero-discount rising-price resampling scenario, forwards reduce mean expenditure by USD 304.88 but increase its standard deviation from USD 1,152.45 to USD 1,190.82. A controlled replication with five portfolios per capital condition finds mean contribution differences between financing and self-funding of +1.0635, -0.1406, and -0.2962 experimental USD under low, baseline, and ample capital, respectively. The evaluation distinguishes contract correctness from economic effectiveness under declared economic and failure assumptions; supplier invoices and commercial revenue are unavailable.

Predicting how a patient's vital signs respond to an intervention is a central question in intensive care. World models can do so by learning dynamics as a function of prior actions. However, such models tend to be brittle outside of training data. Clinicians choose drug dosages based on the patient's state, so the association a model learns between dose and outcome runs opposite to the drug's effect, generalizing poorly to out-of-distribution (OOD) dosing practices. Yet, pharmacological information provides the directional effects of different drugs, which are invariant to OOD shifts. To resolve the OOD sensitivity of current ICU world models, we introduce PHYSIO WORLD, which isolates an intervention's effect by evaluating a forward pass twice: once under recorded doses, and once with those doses set to zero. The difference is projected onto pharmacologically admissible effect directions stated by 70 rules over 28 drugs, leaving the magnitude to be learned from data. Across five distribution-shift parameters over cohorts from three intensive-care databases, and against forecasters, counterfactual models, and invariance objectives, PHYSIO WORLD attains the lowest OOD RMSE in every setting, improving on the strongest external baseline by 8-12%, while matching the in-distribution error of its backbone. Reversing the pharmacological directions degrades accuracy below the backbone, and data-mined directions recover almost no gain, indicating the improvement derives from the content of the pharmacological knowledge. The construction may extend to other settings where the sign of an effect is known in advance and its magnitude is confounded by treatment assignment.

Synchronization among coupled oscillators – from neurons to power grids – is a universal signature of collective behavior, classically measured by the Kuramoto order parameter. Applied identically across five asset classes and 61 financial instruments, a Kuramoto-style cross-timeframe coherence measure detects structure that a calibrated, heteroskedasticity-robust variance-ratio test of the random-walk hypothesis does not: the two diagnostics are statistically independent even on the same price windows. Here we explain why, and extract the physics behind it. The four-state regime alphabet underlying the measure is a Z4 clock model whose exact factorization into two Ising sectors is precisely the order parameter's decomposition into a direction channel and a volatility channel, and the sign-flip symmetry of returns acts on the regime circle as a reflection, yielding a parity selection rule: the direction channel is provably independent of the variance ratio and of every statistic built from squared returns – confirmed by controlled simulation on processes with and without genuine persistence. Boltzmann inversion of the regime statistics then yields effective couplings between adjacent timescales, benchmarked against matched random-walk, GARCH, and fractional-Gaussian-noise nulls: the direction sector's coupling never exceeds its random-walk null in a single instrument, and its deficit independently re-measures the panel's Hurst exponent, while the volatility sector's coupling exceeds every null in every instrument and survives across scale separations where GARCH cannot – a volatility cascade. A closed-form mean-field analysis places markets deep below the synchronization transition, with all genuine cross-scale structure confined to the even, volatility sector.

Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM). The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework. However, their conventional collocation-based implementation (C-NEM) often suffers from physically inadmissible displacement oscillations, integration errors, and high computational costs from automatic differentiation. This work introduces the mesh-based neural energy method (M-NEM), extending the NEM through a mesh-based discretization of the displacement field. By interpolating nodal displacements via shape functions, the M-NEM imposes a kinematic constraint that suppresses oscillations. Furthermore, the method replaces automatic differentiation with algebraic shape function derivatives for strain computation and employs high-order Gaussian quadrature for accurate energy integration. On a directly comparable benchmark problem, the M-NEM reduces stress errors by up to three orders of magnitude relative to the C-NEM while being one to two orders of magnitude faster. On two further benchmarks involving extreme stiffness contrasts, only the M-NEM converges. A comparative study of neural architectures reveals that radial basis function neural networks (RBFNNs) yield optimal performance within the M-NEM, resolving sharp gradients at material interfaces with higher accuracy than multi-layer perceptrons (MLPs) with random Fourier feature (RFF) mapping and faster convergence than Kolmogorov-Arnold networks (KANs).

The global challenge of climate change has driven significant steps to reduce CO2 emissions, guided by international agreements like the Paris Agreement of 2015. Acting too slowly could result in future losses and reputational damage, while moving too quickly could jeopardize shareholder value due to the marginal profitability or potential losses due to technology immaturity of many renewable projects. To navigate this complex transition, energy companies must adopt Sequential Decision Making (SDM) strategies to maximize value creation from decision flexibility under uncertainties. To support this, we developed a custom simulation environment to model the dynamic energy landscape up to 2050. Building on this, we designed a multi-criteria SDM framework that explores various decision strategies related to different portfolios for allocating funds across three sectors: oil & gas, renewables, and CO2 reduction. It aims to maximize value during the transition while accounting for uncertainties in productions, energy prices, and costs. This framework has three objectives: maximizing profit, minimizing CO2 social costs, and enhancing competitive advantage in the renewable energy sector. This research evaluates the use of Reinforcement Learning (RL) to identify optimal investment policies within the defined SDM framework. The agent's sequential decisions shape a virtual dynamic environment by influencing key variables such as oil and gas production, renewable energy output, CO2 emissions, and revenues. Through repeated interaction, the RL algorithm explores the state space and learns an optimal policy under uncertainty. We benchmark the RL strategy against a set of manually defined baseline policies and find it consistently outperforms them in adaptability and long-term value creation.

Neural surrogates for vector-valued partial differential equations can fit training data yet change their predictions when the same physical state is expressed in a rotated coordinate frame. We study this failure on three-dimensional Navier–Stokes dynamics observed at irregularly placed points. We introduce the Invariant-Conditioned Isotropic Kernel Neural Operator (IKNO), a compact graph model that builds local interactions from scalar quantities unchanged by rotation and vector directions that rotate with the data. Consequently, rotating the positions and velocities rotates the predicted velocity change in exactly the same way. On a held-out test set fixed after model design, training unconstrained graph models on randomly rotated examples reduces but does not eliminate their coordinate dependence. In contrast, IKNO is consistent to numerical precision, matches the forecasting accuracy of a general rotation-aware Tensor Field Network with $5.6$ times fewer parameters, and outperforms a parameter-matched graph simulator. These results show that a compact, PDE-specialized model can remove coordinate dependence without sacrificing forecasting accuracy.

Rapid and accurate prediction of urban wind and temperature fields is important for urban microclimate design and climate adaptation. Large-eddy simulation (LES) effectively resolves these instantaneous fields, but its application is limited in iterative design of urban microclimate applications due to high computational cost. Existing regressive data-driven models offers quick outputs, but they produce only deterministic point predictions that inherently fail to represent turbulent stochasticity. This paper adopts a novel generative framework of Conditional Flow Matching (CFM) that uses building geometry and mean flow as guidance to generate plausible three-dimensional instantaneous velocity and temperature fields for urban microclimate in seconds. To overcome the GPU memory bottleneck of pixel space 3D generation, the model operates in parallel on overlapping pixel space through a shared-noise initialization that preserves high spatial continuity of flow structure across the entire domain. Against reference LES data, the CFM surrogate can rapidly and accurately restore the first-order statistics with Normalized Root Mean Square Error (NRMSE) of 2.99% for wind and 1.77% for temperature, second-order turbulence metrics with NRMSE of 7.17% for wind and 8.84% for temperature, turbulent kinetic energy with NRMSE of 7%, probability density function and vertical profiles in representative locations. Wind engineering application of local gust prediction demonstrate that the speed and accuracy of CFM, supporting the use of generative AI for making turbulence-aware resilient urban design and climate adaptation more computationally feasible.

Short-horizon realized volatility forecasting requires the integration of market information that evolves at incompatible temporal resolutions, from second-level order book dynamics to weekly regime drift. Our conference work introduced HAN-T, a hierarchical architecture in which scale-specific Transformer encoders process short, mid, and long-horizon streams and a learned attention fuser weighs their contributions. This article replaces the quadratic attention encoders with selective state space (Mamba) encoders while retaining attention only in the fuser, where the input is a three-token set rather than a long sequence. The resulting hybrid, HAN-Mamba, summarizes each stream through a recurrent state whose input-dependent gating matches two structural properties of volatility: persistent but decaying memory and abrupt regime shifts. On the Optiver Realized Volatility Prediction benchmark under time-aware five-fold cross-validation, HAN-Mamba improves mean RMSPE over HAN-T (0.1942 vs. 0.1965) with 33% fewer parameters. Its linear-time encoders further allow the high-frequency context to be extended from 60 to 240 buckets, reducing error to 0.1927 where the attention variant saturates, and support constant-time streaming updates at inference. Ablations attribute the gains to the encoder swap, confirm that the hierarchical prior transfers across sequence-model families, and show that the permutation-invariant attention fuser remains the correct mechanism for cross-scale integration.

The quantification of three-dimensional human kinematics is fundamental to neurorehabilitation and musculoskeletal research, yet atypical posture, physical assistance, and rapid movement create conditions of partial observability. Here, we evaluate a latent-structure-informed framework combining convolutional rank-reduction autoencoding with feedforward regression to reconstruct movement from synchronized video. Three case-based demonstrations span therapist-assisted sit-to-stand in a child with cerebral palsy, unassisted sit-to-stand in a typically developing child, and multidirectional single-leg hopping in a young adult. Reconstruction was examined through positional trajectories, projected angular descriptors, and hip-knee coupling. Across test repetitions excluded from model training, mean absolute errors in a predicted marker position during assisted sit-to-stand ranged from 12.02 to 57.11 mm. Sagittal knee and trunk descriptor errors were 5.32{\deg} and 5.38{\deg} in the typically developing case. Hip-knee cyclograms captured aspects of coupled-motion patterns in both cases, with closer trajectory correspondence in the typically developing case. Sixteen test hops yielded a vertical knee-marker mean absolute error of 15.58 mm. These findings connect latent-structure-informed reconstruction with biomechanically interpretable movement features, providing a foundation for video-derived assessment spanning clinically atypical movement and high-dynamic athletic movement.

Accurate forecasting models are usually large, expensive to update online, and fixed in architecture once trained. We apply ONE-NAS, an online neuroevolutionary architecture search that evolves a population of small recurrent networks as each window of data arrives, to daily cross-sectional stock return prediction, and pilot it on a host and endpoint pipeline: the host runs the search and ships each generation's champion genomes over TCP/IP to a Raspberry Pi 4B, which predicts online. On the Pi a single champion predicts a 50-stock window in 24.6~ms and the ensemble of 40 island champions in 556~ms, far inside the daily decision cycle. On four panels of US mid-cap equities over 2022–2024, reading the population as a rank-mean ensemble of island champions returns $+27.5\%$ net of realised transaction costs, against $+11.3$ to $+14.8\%$ for online LSTM, online GRU and monthly-retrained LSTM baselines and $+4.5\%$ for the single best genome used in prior ONE-NAS work.

We develop a hybrid pore-network model (PNM) for discrete microbubble transport coupled to connected two-phase flow in porous media. We apply the model to simulate flow in the porous transport layer of a rotating proton exchange membrane (PEM) electrolyser. At sufficiently large apparent gravitational forces, bubbles growing at the catalyst layer can detach at sizes smaller than the characteristic pore size and move through liquid-filled pores via buoyancy and advection. The model couples a dynamic two-phase PNM to a Lagrangian bubble tracker. Pore-scale Stokes simulations in square throats provide closures for the bubble buoyancy velocity, the hydraulic resistance of bubble-occupied throats, and the reciprocal coupling between liquid flow and bubble motion. Verification tests assess conservation, pressure-flow coupling, bubble growth, advection, merging, trapping, and transfer to the connected gas phase. The network simulations show that increasing apparent gravitational forces shifts a larger fraction of the produced gas toward discrete-bubble transport. The increase mostly comes from a reduced detachment radius, which decreases bubble size and lets them move more freely through the network.

Ship internal arrangement is a complex spatial design problem in which competing functions within a fixed volume affect spatial relationships, mass distribution, trim, and stability. Exploring these trade-offs requires many layouts in a common format, yet public general-arrangement drawings are scarce, inconsistent, and two-dimensional. This study develops a common framework for generating conceptual 3D internal arrangements across six vessel families: bulk carriers, tankers, container vessels, offshore support vessels, patrol vessels, and yachts. Each arrangement uses paired voxel grids and topological graphs for spatial and connectivity analysis. The framework is evaluated through three experiments: (i) comparison of 50,000 generated arrangements with 23 reconstructed real references, (ii) envelope-constrained reconstruction of one reference per family, and (iii) response of generated layouts to requested function volumes. Generated design spaces broadly align with references within each family's sampling range. Searching alternative spatial subdivisions improves reconstruction across all families, with voxel accuracy reaching 75.5%. Fuel and ballast allocations respond near-proportionally to requested volume, while other functions depend on subdivision capacity, compartment eligibility, and discrete assignment. A fixed-hull offshore support vessel application shows that the same hull and requested programme can produce different adjacency and trim outcomes, with five nondominated concepts among 119 of 500 alternatives meeting stability and programme criteria. The results support layout design-space exploration across vessel families and changing requirements, with spatial organisation remaining important beyond volume compliance. The generator and conceptual general arrangement dataset are released publicly for reproducible analysis, benchmarking, and learning-based design studies.

Biventricular repair is favored for children with complex double-outlet right ventricle (DORV) to eliminate the long-term morbidity of single ventricle physiology. However, creating a baffle that maintains adequate cross-sectional area while limiting incursion on the tricuspid valve apparatus is challenging in a distorted, arrested heart. Three-dimensional (3D) models have aided baffle design with anatomic visualization but analytic approaches, including computational fluid dynamic (CFD) simulation support, have not yet been incorporated into clinical workflows. We present the preoperative, prospective construction of a DORV repair baffle guided by a semi-automated area-preserving algorithm and CFD analysis.