Computational Engineering
A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation
Yuzhou Zhao, Han Zhang, J. Matias Di Martino et al. (+2 more)
Fast and accurate simulation of hemodynamic behavior within vascular networks is essential for numerous clinical applications. However, obtaining high-quality and computationally efficient flow measurements across complex vascular networks remains challenging. To address this, we first decompose the vascular network into a set of bifurcation units and then develop an operator network capable of mapping unit-specific parameters to the local solution fields of each bifurcation unit. By lumping the Windkessel-model outlet parameters and incorporating inlet boundary conditions from the solution of parent units, the flow and pressure fields can be rapidly approximated. Subsequently, operator-network-driven Schwarz waveform relaxation is applied across bifurcation units to correct discontinuities and improve numerical accuracy. On 7-segment and 55-segment arterial tree models, the proposed method achieves $13\times$ to $17\times$ wall-clock speedups over conventional 1D numerical simulation, with relative $L^2$ errors of 1% in both pressure and velocity. The resulting pulse wave velocity biomarkers agree with the conventional reference to within 1–2%, and the same trained operator generalizes to different tree-like 1D vascular network
topologies.
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All authors Yuzhou Zhao, Han Zhang, J. Matias Di Martino, Jean-Michel Morel, Guillermo Sapiro
Computational Engineering
SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Trucks
Riddhiman Raut, Yin Yu, Aashwin Anand Mishra et al. (+4 more)
Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics
datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such
dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million
cells at a Reynolds number of $1.4 \times 10^7$ and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and
benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a
benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.
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All authors Riddhiman Raut, Yin Yu, Aashwin Anand Mishra, Michael Emory, Thomas Economon, Peter Lyu, Juan J. Alonso
Computational Engineering · Cross-listed from cs.AI
AIM: Agentic Idea Management for Automated Research
Hyeong Kyu Choi, Bhavana Dalvi Mishra, Jiefeng Chen et al. (+7 more)
Frontier LLMs are increasingly used to automate scientific research through iterative search. We distinguish idea-driven search from solution-driven search and identify three core challenges: organizing evolving research ideas, selecting promising directions, and maintaining
alignment between ideas and their implementations. To address these challenges, we introduce the Agentic Idea Manager (AIM), a fully autonomous framework for managing and exploring research directions in idea-driven automated research. Inspired by
Bayesian optimization, AIM uses an Agentic Surrogate and an Agentic Acquisition mechanism to organize discovered ideas and guide their selection. A Solution Auditor maintains idea-solution integrity, while a Resource Planner adaptively allocates the remaining experimental budget across parallel search branches. Experiments on 10 AutoLab
benchmark tasks show that AIM surpasses the strongest baseline by 1.6 percentage points on System Optimization tasks and 4.9 percentage points on long-horizon Model Development & CUDA tasks. Notably, AIM reaches the best baseline performance up to 3.1x faster in wall-clock time. We further provide a theoretical analysis of when searching over ideas becomes beneficial. Our analysis shows that explicit idea-level allocation makes semantic coverage directly controllable, and that broader coverage becomes increasingly valuable when competitive research directions are sparse among many plausible alternatives. Project Page: https://imhgchoi.github.io/agentic-idea-manager/
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All authors Hyeong Kyu Choi, Bhavana Dalvi Mishra, Jiefeng Chen, Mihir Parmar, Rui Meng, Chun-Liang Li, Xiangru Tang, Sharon Li, Jinsung Yoon, Tomas Pfister
Computational Engineering
Reduced order modeling for micromorphic computational homogenization of mechanical metamaterials with patterning fluctuation fields
Theron Guo and Ondřej Rokoš
Mechanical metamaterials owe some of their exotic effective properties to microstructural instabilities such as buckling and pattern transformation. Their fine-scale geometry, combined with the interplay of local and nonlocal effects, renders direct numerical simulation (DNS) prohibitively expensive, if not intractable. Micromorphic computational homogenization~\citep{Rokos2019} has been proposed to make macroscopic simulations feasible: a representative volume element (RVE) carrying patterning fluctuation fields resolves the microscale, while an effective micromorphic continuum describes the macroscale. Such simulations nevertheless remain costly, since the RVE problem and its associated tangent problems must be solved at every macroscopic integration point, which becomes prohibitive, especially in three dimensions. We therefore propose a reduced order model for the microscopic problem, combining proper orthogonal decomposition with a hyperreduction method tailored to the micromorphic setting. Two numerical examples quantify the reduced basis and hyperreduction errors and discuss the offline costs and attainable online speed-ups. The results show that this approach can enable engineering-scale large deformation analysis of mechanical metamaterials.
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Computational Engineering
Neural topology optimization of ship structures under propulsion machinery vibrations
Shengyu Yan, Muhammad Muztahidul Hakim Zareer and Jasmin Jelovica
Ship structural vibrations contribute to noise, fatigue, and equipment damage, while dynamic-compliance
topology optimization can produce pathological designs near resonance. This study extends neural-reparameterized
topology optimization using a convolutional Kolmogorov-Arnold network (KATO) to forced-vibration design with active input power (AIP) as the objective. Applications include a 100 Hz engine-supporting deck panel and an 18 Hz thruster foundation frame. Helmholtz PDE filtering and Heaviside projection control feature sizes and manufacturing tolerance. Across both deck families, all eight optimized layouts reduce AIP relative to size-optimized references and, after finite-depth extrusion, also achieve lower static compliance. For unrestricted, manufacturing-aware, and stress-aware frame variants, KATO matches GCMMA in AIP within 0.5 dB while yielding 22-36x lower static compliance after matched-volume binary re-analysis. In a near-resonant 300 Hz case, both methods reduce initial AIP by more than 32 dB; KATO maintains a connected design, achieves 59x lower binary static compliance, and reduces maximum AIP over 1-500 Hz by 2.7 dB. KATO runs 6.4-10.4x faster than GCMMA for the implemented stress-aware formulations. The results demonstrate neural AIP-driven
topology optimization as an efficient approach for designing connected, feature-size-controlled ship structures with improved forced-vibration performance.
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Computational Engineering
Active Liquidity On Chain: Evidence from PropAMMs Across Chains
Ozan Solmaz, Lioba Heimbach and Jason Milionis
The liquidity providers of most typical automated
market makers (AMMs) are passive and known to suffer from adverse selection. AMMs traditionally rely on trades executed on them to sync the price with external
markets (and a notion of fair value thereof). As a result, when an external fair value moves, arbitrageurs trade on AMMs to pick off their stale quotes. A recent approach termed proprietary automated
market makers (propAMMs) emerged as a response in 2024: these on-chain programs instead have their singular operator quote from its own inventory, repricing without a trade via efficiently provided price updates. By 2026, propAMMs accounted for more than half of SOL/USDC volume on Solana. We present the first year-long longitudinal measurement of propAMMs on Solana, Base and Monad, and decode the on-chain logic of the dominant propAMM on Base. We find that two seconds after a fill, propAMMs earn 0.37 bps on Solana and 1.19 bps on Base, while AMMs lose 0.22 and 0.62 bps. We empirically quantify and classify their edge as stemming from four factors: propAMMs continuously reprice rather than waiting for a trade, they charge for the source-dependent risk each counterparty might bring, they avoid cross-venue arbitrage from other on-chain
markets (such as other AMMs), and they spoof by filling trades at a worse price than they quote. Finally, we show that on our proxy for retail flow (i.e., fills that arrive when the reference price is not moving) propAMMs collect 0.26 bps on Solana where AMMs collect 2.59 bps, indicating that they offer better prices for short-term uninformed flow.
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Computational Engineering · Cross-listed from cs.NI
Pricing IoT Data Delivered via LEO Satellites
Rahul Ramachandran and Suman Banerjee
IoT terminals served by LEO satellite constellations transmit data to passing satellites in discrete uplink windows. That data is delivered to buyers only when the satellite reaches a ground station. This store-and-forward structure makes the achievable price a discontinuous function of the delivery completeness threshold (a phenomenon we call a pricing cliff) and creates a geographic pricing asymmetry between polar and equatorial terminals that depends on constellation size. We present an integrated pricing model combining a full SGP4 orbital simulation of the deployed Kinéis constellation with a buffer flow model and a value decay framework with decay constants derived from operational decision-window timescales in the application literature and anchored to observed satellite imagery
market prices. We show that polar and equatorial terminals are dominated by structurally different latency components requiring different infrastructure interventions, formally characterize the pricing cliff phenomenon and its commercial significance, and derive a geographic pricing premium that is exactly independent of the residual value assumption. Going from 1 to 25 satellites reduces the polar–equatorial premium by 25x, with diminishing returns beyond n=10; at full constellation size the premium falls below 1% of peak data value and remains below 1.5% across the full plausible range of buyer urgency.
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Computational Engineering · Cross-listed from q-fin.CP
From Intraday Orderbook to Imbalance Price: Understanding Cross-Market Interaction
Runyao Yu, Jochen L. Cremer, Pierre Pinson et al. (+4 more)
Power systems with increasing variable renewable generation face greater uncertainty in scheduling and balancing. Intraday and balancing electricity
markets facilitate position adjustments and real-time balancing close to delivery. As delivery approaches, continuous intraday
market participants exposed to imbalance settlement adjust their positions by trading additional volumes to reduce their imbalance exposure. We
conjecture that positions remaining open after intraday trading, together with demand and supply uncertainties affecting physical
market participants, influence price formation in the balancing
market. This cross-
market interaction is, however, rarely studied. To understand this interaction, this paper uses probabilistic modeling to examine how intraday orderbook information reflects subsequent imbalance price formation in Germany and Austria. We compare orderbook representations based on open, high, low, close, and volume, Volume-Weighted Average Price (VWAP), and last mid price across multiple horizons. Each representation is evaluated using the self product, neighboring products, and the product from the neighboring country. We then compare the best orderbook setting with fundamental feature sets and their combinations, followed by an ablation study of the available training history. We show that VWAP with neighboring products provides the best performance in both countries. Combining orderbook and fundamental information reduces testing loss in Germany but increases it in Austria. Using all available observations provides the best overall performance, while excluding 2022 can reduce loss for extreme price samples. These results reveal and help explain country-dependent interactions between the intraday and balancing
markets.
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All authors Runyao Yu, Jochen L. Cremer, Pierre Pinson, Jalal Kazempour, Leo Semmelmann, Takuji Matsumoto, Derek W. Bunn
Computational Engineering · Cross-listed from cs.AI
Co-PiLOT: Constrained Physics-Informed Latent Optimization for Target-Driven Inverse Design
Mahish K. Guru, Mayank Nagar, Ayush vyas et al. (+3 more)
Inverse design of physical systems (molecules, devices, microstructures) often reduces to optimizing a high-dimensional structure against an expensive black-box simulator. Direct search is difficult because the space is non-Euclidean, feasibility is hard to encode, and each evaluation is expensive. We present Co-PiLOT, a latent optimization approach that maps candidates through a generative encoder-decoder, uses the decoder as a learned validity prior, and searches the latent space with physics-informed black-box optimization. The framework is applied on the inverse design of magnesium
alloy microstructure/texture. We develop a
vision transformer based-encoder; paired with latent
diffusion,
diffusion transformer and rectified-flow
transformer-based decoders on $\sim80{,}000$ EBSD-derived microstructure
dataset to learn a minimal bottleneck, $z$. The ViT-FMDiT model ($z$=$768$) reconstructs high-fidelity microstructure images (FID $27.86$, MS-SSIM $0.178$), which our self-segmenting orientation codec converts into input grids for
crystal plasticity solver. Finally, we introduce MERIDIAN, an active latent optimizer driven by deep-kernel Gaussian-process uncertainty, failure-aware feasibility prediction,
manifold-aware trust regions, and target-aware acquisition. Within a budget of $160$ simulations, the ViT-FMDiT and MERIDIAN combination yields the best target-driven objective score, reducing the relative target error by $3$–$22\%$ against seven baselines (DANTE, TuRBO, BAxUS, CMA-ES, DDOM, SEIKO, DDPO) on the same decoder.
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All authors Mahish K. Guru, Mayank Nagar, Ayush vyas, Jan Bohlen, Roland Aydin, Noomane Ben Khalifa
Computational Engineering · Cross-listed from cs.CR
Making Duplicate Reimbursement Unrepresentable: A Verified Ethereum E-Invoice System for Humans and AI Agents
Jia Cai
Electronic invoices are replacing paper invoices worldwide, but today's centralized architectures leave three problems unsolved on the consumption side: an invoice can be submitted for reimbursement repeatedly, authenticity is difficult for recipients to verify, and data is siloed at a central authority that forms both a performance bottleneck and a single point of failure. This paper presents the design, formal analysis, and implementation of a complete blockchain-based electronic invoice system on Ethereum. We formalize the invoice lifecycle as a guarded labeled transition system and prove, under standard cryptographic and consensus assumptions, that the system guarantees: (i) reimbursement uniqueness–an invoice is reimbursed at most once, even across mutually distrusting organizations; (ii) face integrity–any verified invoice matches the recorded one unless keccak256 second-preimage resistance is broken; and (iii) authorization soundness for every lifecycle operation. The core invariants are machine-checked using Solidity SMTChecker, proving inductive validity across all reachable transaction sequences. The architecture models each invoice as a non-fungible, non-tradable
token whose state transitions through five guarded subsystems, employing a lock-based protocol that makes duplicate reimbursement unrepresentable rather than merely detectable. We implement the design as a Solidity 0.8 contract with a four-role web application and evaluate it on a private Ethereum network: issuing costs 646,773 gas, full reimbursement costs under 135,000 gas, all operations run in O(1) time, and a single node sustains 137 issuances/s. Finally, the verified contract serves as a safety envelope for LLM-based reimbursement
agents, provably rejecting unsafe actions (duplicate, over-limit, or forged-receipt claims) even when the
agent's internal policy fails. All code and
benchmarks are open-source.
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Computational Engineering · Cross-listed from cs.AI
MeanFlowAdvantage: Stable Reward Fine-Tuning for Few-Step Average-Velocity Generators
Haocheng Tang, Tianchi Xie and Xingqiao Lin
MeanFlow enables efficient few-step generation by predicting interval-average velocities, but this representation creates a mismatch for reward fine-tuning: existing advantage-based objectives are typically defined on instantaneous velocities or equivalent $x_0$-space predictions, whereas inference directly uses the learned average-velocity map. We introduce MeanFlowAdvantage, a signed advantage-weighted least-squares objective for average-velocity generators. Our key construction uses a shared, detached MeanFlow derivative correction to express the reward objective in prediction space while making rollout and reference regularization exact penalties on the average-velocity network deployed at inference. The resulting formulation preserves MeanFlow's native few-step sampler and provides a direct mechanism for transferring reward improvements to the deployed flow map. On SD3.5-Medium, MeanFlowAdvantage improves all eight reported metrics over the matched four-step MeanFlowNFT baseline and, with only four NFEs, matches or exceeds the 40-step DiffusionNFT baseline on six of eight metrics. The same objective also transfers to DNA promoter design, where it supports both teacher-free on-policy RL for a generator defined on a
manifold and teacher-guided reward-graded
distillation, with the latter yielding the lowest one-step Sei profile MSE among the compared configurations.
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Computational Engineering
A Three-Layer Framework for Measuring Names and Its Census Application on a Token Launchpad
Dingding Cao, Yujing Zhong, Han Wang et al. (+3 more)
Asset names influence
market behavior, yet standardized name measurement remains lacking. Existing processing fluency measures focus mainly on alphabetic
languages and are unsuitable for Chinese names. Cultural meanings usually require manual coding, limiting large-scale analysis, while name competition through reuse and semantic crowding remains underexplored. This study constructs a
dataset of 513,647 naming attempts from the Four
token launchpad on BNB Chain between February and June 2026 and proposes a three-layer framework for name measurement. The form layer measures linguistic fluency using 38 Chinese-oriented features. The reference layer captures cultural meanings through human coding and large
language model expansion with reliability evaluation. The relation layer measures name reuse, semantic crowding, and lexical variation. The three layers are largely independent, with correlations below 0.11. Census analysis reveals that name diversity follows Heaps' law, new-name adoption declines over time, name reuse shows heavy-tailed patterns, and repeated naming occurs at distinct creator-level and cross-creator time scales. Cultural events also trigger rapid naming responses. The framework, annotated
dataset, and code are released to support scalable analysis of naming behavior in digital
markets and other naming environments.
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All authors Dingding Cao, Yujing Zhong, Han Wang, Xian Pan, Rizwan Akhtar, Wei Yang
Computational Engineering
Hybrid GA/MSDLO Approach to Solve a Greenfield Robotized Machine Tending Layout
Ramez Awad and Joshua Beck
Meta-heuristics like genetic
algorithms (GAs) effectively explore solution spaces but often yield suboptimal results and are sensitive to parameter tuning. In contrast, the mass-spring-damper layout optimization (MSDLO) method is fast and excels in locally optimizing resource arrangements, though its effectiveness depends on the initial resource placement. This paper first employs genetic
algorithms to establish an optimal resource placement in a greenfield layout. We then apply MSDLO to fine-tune the positions and orientations of these resources. The results are presented and discussed, highlighting this approach's practicality in effectively addressing industry needs.
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Computational Engineering
Explainable and Trustworthy AI for Anti-Money Laundering: A Graph-based Hybrid Framework for Real-World Financial Crime Detection
Ali Shahbazi, Faraz Sasani, Arshia Hossein zadeh et al. (+2 more)
Purpose: Money laundering threatens financial systems, while rule-based monitoring suffers from high false-positive rates and limited ability to capture relational transaction patterns. This study proposes an explainable graph-based framework for anti-money laundering (AML) detection that jointly addresses predictive performance, explanation faithfulness, and uncertainty calibration. Methods: Using the IBM Transactions for Anti-Money Laundering (HI-Small)
benchmark, comprising 5,078,345 transactions among 518,573 accounts with 0.10% illicit transactions, a directed attributed graph with 4,487,133 edges was constructed using temporal, leakage-safe partitioning. Three GATv2 architectures, BASE, BASE-Large, and IMPROVED, incorporating bidirectional message passing, edge updates, and port-aware features, were compared with XGBoost and Random Forest using identical features. The best model was evaluated using GNNExplainer against documented typologies and Mondrian conformal prediction for uncertainty calibration. Results: IMPROVED achieved the strongest performance (AUPRC = 64.85%, Best F1 = 68.42%), exceeding BASE-Large by 30.65 AUPRC points and XGBoost (AUPRC = 38.46%) by 26.4 points. The proposed mechanisms contributed more than capacity scaling alone. GNNExplainer recovered documented typologies with higher fidelity than
attention-weight and random baselines (mean Jaccard overlap: 21.4% vs. 1.0%, p < 0.001). Mondrian conformal prediction achieved coverage close to the 90% nominal target with an average prediction-set size near one. Conclusion: Explicit transaction
topology modeling substantially improves AML detection, while faithful explanations and calibrated uncertainty support interpretable, human-in-the-loop compliance decision-making.
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All authors Ali Shahbazi, Faraz Sasani, Arshia Hossein zadeh, Sheyda safaeimoradi, Hossein Najafzadeh
Computational Engineering
FinRegQA-EU: Corruption-Based Preference Data for Grounded EU Financial Regulatory Question Answering
Aulia Kharis Rakhmasari, Fan Yu, Alexander Hoyle et al. (+1 more)
Large
Language Models (LLMs) struggle with region-specific factual knowledge, particularly in financial regulation. While
benchmarks such as CFinBench, provide broad coverage of financial knowledge in other regions, no comparable resource exists for European financial regulation. We close this gap by proposing an end-to-end pipeline for evaluating and improving LLMs on European financial regulatory question answering. Our
dataset is grounded in the official Q&A corpora of the European Banking Authority (EBA) and the European Securities and
Markets Authority (ESMA). We evaluate candidate answers with a pointwise LLM-as-a-Judge protocol using three judges from distinct model families, retain only unanimously judged pairs, and sharpen the rejected side through a taxonomy of regulatory failure modes : law swaps, article swaps, hallucinated citations, and hallucinated text. By fine-tuning on the resulting preference pairs exposes a divergence at the core of our findings: supervised fine-tuning attains the highest judge score of any method yet got the lowest rule-based Citation F1. SFT is producing longer answers with three times as many citations, most of them unsupported. DPO and GRPO offer the better trade-off with more concise answers and the highest citation F1 among fine-tuned models. Standard LLM-as-a-Judge evaluation rewards citation density as evidence of grounding and cannot detect when those citations are fabricated. Thus, we detect a blind spot that matters wherever answers must be verifiable. We release the
benchmark and evaluation stack at https://github.com/auliakharis/FinRegQA-EU.
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All authors Aulia Kharis Rakhmasari, Fan Yu, Alexander Hoyle, Elliot Ash
Computational Engineering
Frontier Autolab: Organizational Memory, Adversarial Dissent and Temporal Leakage in Multi-Agent LLM Firms Across Fifty Years of Technological Change
Bravish Ghosh
Multi-
agent LLM systems are increasingly structured like organizations, with roles, critics and shared
memory, yet they are evaluated on tasks that last minutes. We ask how such an organization behaves when the ground it stands on keeps moving. Frontier Autolab is a long-horizon testbed in which one simulated firm, voiced by sixteen role personas and a dedicated Red Team, must re-found itself in nine technology eras from 1990 to 2040. Each era is temporally gated: the firm decides from a dated briefing, a historian-judge then reveals what happened and scores the decision on a five-dimension rubric, and lessons enter a persistent Playbook. Six eras are scored against history, one against the live
market and two are open forecasts. Across four trajectories (36 era decisions, 180 subscores) we find a consistent foresight-commitment gap: in all 24 historically scored eras the judge rated the firm's recognition of the coming shift above its choice of where to build (mean gap 1.9 points on a 10-point scale), because boards chose the layer their existing assets could reach. Organizational design shaped long-run character. A Red Team armed with numeric kill gates produced fifty years of gated pilots and no product, and the rubric rated this firm highest; firms whose
memory stored
market-structure lessons pivoted every era, while a firm whose
memory stored only validation procedure kept one method throughout. We also show why such results are hard to trust. Scores rise across eras in every run while the judge's own hindsight subscore falls (within-run r = -0.58), so apparent learning is confounded with recall of history, and we trace further distortions to self-judging, briefing selection and score aggregation. We release all records and an API harness, and specify fictional and post-cutoff eras that would turn the testbed into a
benchmark.
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Computational Engineering
Interpolating Neural Operator (INO): A Data-Free and Efficient Approach for Learning PDE Solution Operators
Jiachen Guo, Ye Lu, Naichen Shi et al. (+2 more)
Neural operators have become a popular approach to approximate the solution operators of parametric partial differential equations (PDEs). However, existing neural operators either require a large amount of simulation data or a long physics-informed training on GPUs, and they cannot tell how accurate an individual prediction is. In this paper, we propose the Interpolating Neural Operator (INO), a data-free interpolating neural network that is trained directly on the weak form of the PDE. In INO, the Karhunen-Loève coordinates of the input field are treated as additional inputs together with the spatial coordinates, and each input is approximated by a C-HiDeNN sub-network whose trainable parameters are nodal values. Since the network is multilinear in its parameters, training reduces to a sequence of one-dimensional linear solves by greedy alternating least squares. As a result, INO trains on one CPU core and predicts a new solution in microseconds. For coercive problems, the total error of every prediction is bounded by a computable residual bound that requires no reference solution, and the same bound applies to the predictions of other methods that satisfy the boundary conditions exactly. Before each prediction, INO checks whether the leading coordinates of the input lie within the range on which it is trained, and inputs outside this range can be passed to a conventional solver or to an INO trained on a wider range. INO is compared with physics-informed FNO and DeepONet on different
benchmarks. INO is the most accurate model on most of these problems, by 15$\times$ on two-dimensional Helmholtz at $65^2$ and 53$\times$ on the
diffusion-reaction
benchmark, and on the one- and two-dimensional problems its training on one CPU core takes 3-80$\times$ less time than the physics-informed baselines on one GPU.
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All authors Jiachen Guo, Ye Lu, Naichen Shi, Thomas J.R. Hughes, Wing Kam Liu
Computational Engineering
Decompose Dynamics Before Learning Dependencies in Spatiotemporal Systems
Ziqi Wang, Daojiang Hu, Cheng Bao et al. (+4 more)
Relations in networked spatiotemporal systems are often learned from observations that entangle dynamics governed by different mechanisms, obscuring what evolves locally and how it propagates across nodes. We introduce Component-Aware Network Dynamics with Ordered Relations (CANDOR), which decomposes local dynamics before learning their dependencies. CANDOR represents each trajectory through a persistent background, gradual accumulation and release, and sparse shocks. Conditioned on these components, a delay-aware physical branch models edge and sample-dependent propagation over directed
topology, while a
topology-unconstrained functional branch discovers latent dependencies from background dynamics. Context-adaptive fusion combines functional, forward-propagation, and reverse-support forecasts, with training objectives encouraging specialized and semantically consistent representations. Experiments on two traffic
benchmarks and three long-horizon water-quality
datasets span two distinct spatiotemporal systems: human-driven urban traffic and naturally evolving river water quality. CANDOR consistently outperforms the strongest baselines, reducing MAE by up to 4.31% for traffic and MSE by up to 5.47% for water-quality forecasting. These results establish decomposition before dependency learning as an effective principle for spatiotemporal representation learning.
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All authors Ziqi Wang, Daojiang Hu, Cheng Bao, Zhiwei Ling, Wenzhuo Qian, Jiahui Zhai, Hailiang Zhao