Jian Cheng Wong, Isaac Yin Chung Lai, Pao-Hsiung Chiu, Chin Chun Ooi, Abhishek Gupta, Yew-Soon Ong
Physics-informed neural networks (PINNs) have garnered significant interest for their potential in solving partial differential equations (PDEs) that govern a wide range of physical phenomena. By incorporating physical laws into the learning process, PINN models have demonstrated the ability to learn physical outcomes reasonably well. However, current PINN approaches struggle to predict or solve new PDEs effectively when there is a lack of training examples, indicating they do not generalize well to unseen problem instances. In this paper, we present a transferable learning approach for PINNs premised on a fast Pseudoinverse PINN framework (Pi-PINN). Pi-PINN learns a transferable physics-informed representation in a shared embedding space and enables rapid solving of both known and unknown PDE instances via closed-form head adaptation using a least-squares-optimal pseudoinverse under PDE constraints. We further investigate the synergies between data-driven multi-task learning loss and physics-informed loss, providing insights into the design of more performant PINNs. We demonstrate the effectiveness of Pi-PINN on various PDE problems, including Poisson's equation, Helmholtz equation, and Burgers' equation, achieving fast and accurate physics-informed solutions without requiring any data for unseen instances. Pi-PINN can produce predictions 100-1000 times faster than a typical PINN, while producing predictions with 10-100 times lower relative error than a typical data-driven model even with only two training samples. Overall, our findings highlight the potential of transferable representations with closed-form head adaptation to enhance the efficiency and generalization of PINNs across PDE families and scientific and engineering applications.
Matteo Rigoni, Daniele Lanzoni, Francesco Montalenti, Roberto Bergamaschini
Simulations of crystal growth are performed by using Convolutional Recurrent Neural Network surrogate models, trained on a dataset of time sequences computed by numerical integration of Allen-Cahn dynamics including faceting via kinetic anisotropy. Two network architectures are developed to take into account the effects of a variable supersaturation value. The first infers it implicitly by processing an input mini-sequence of a few evolution frames and then returns a consistent continuation of the evolution. The second takes the supersaturation parameter as an explicit input along with a single initial frame and predicts the entire sequence. The two models are systematically tested to establish strengths and weaknesses, comparing the prediction performance for models trained on datasets of different size and, in the first architecture, different lengths of input mini-sequence. The analysis of point-wise and mean absolute errors shows how the explicit parameter conditioning guarantees the best results, reproducing with high-fidelity the ground-truth profiles. Comparable results are achievable by the mini-sequence approach only when using larger training datasets. The trained models show strong conditioning by the supersaturation parameter, consistently reproducing its overall impact on growth rates as well as its local effect on the faceted morphology. Moreover, they are perfectly scalable even on 256 times larger domains and can be successfully extended to more than 10 times longer sequences with limited error accumulation. The analysis highlights the potential and limits of these approaches in view of their general exploitation for crystal growth simulations.
Wujiang Xu, Jiaojiao Han, Minghao Guo, Kai Mei, Xi Zhu, Han Zhang, Dimitris N. Metaxas
LLM agents increasingly operate in open-ended environments spanning hundreds of sequential episodes, yet they remain largely stateless: each task is solved from scratch without converting past experience into better future behavior. The central obstacle is not \emph{what} to remember but \emph{how to use} what has been remembered, including which retrieval policy to apply, how to interpret prior outcomes, and when the current strategy itself must change. We introduce \emph{Agent Evolving Learning} (\ael{}), a two-timescale framework that addresses this obstacle. At the fast timescale, a Thompson Sampling bandit learns which memory retrieval policy to apply at each episode; at the slow timescale, LLM-driven reflection diagnoses failure patterns and injects causal insights into the agent's decision prompt, giving it an interpretive frame for the evidence it retrieves. On a sequential portfolio benchmark (10 sector-diverse tickers, 208 episodes, 5 random seeds), \ael{} achieves a Sharpe ratio of 2.13$\pm$0.47, outperforming five published self-improving methods and all non-LLM baselines while maintaining the lowest variance among all LLM-based approaches. A nine-variant ablation reveals a ``less is more'' pattern: memory and reflection together produce a 58\% cumulative improvement over the stateless baseline, yet every additional mechanism we test (planner evolution, per-tool selection, cold-start initialization, skill extraction, and three credit assignment methods) \emph{degrades} performance. This demonstrates that the bottleneck in agent self-improvement is \emph{self-diagnosing how to use} experience rather than adding architectural complexity. Code and data: https://github.com/WujiangXu/AEL.
Maximilian Westermann, Ben Griffin, Aaron Ontoyin Yin, Zakari Salifu, Yagiz Ihlamur, Kelvin Amoaba, Joseph Ternasky, Fuat Alican, Yigit Ihlamur
Feature discovery from complex unstructured data is fundamentally a reasoning problem: it requires identifying abstractions that are predictive of a target outcome while avoiding leakage, proxies, and post-outcome signals. With the introduction of ever-improving Large Language Models (LLMs), our method provides a structured method for addressing this challenge. LLMs are well suited for this task by being able to process large amounts of information, but unconstrained feature generation can lead to weak features. In this work, we study reasoning control in LLMs by inducing cognitive behaviors for improving feature discovery. We introduce CoFEE (Cognitive Feature Engineering Engine), a reasoning control framework that enforces cognitive behaviors in how the LLM reasons during feature discovery. From a machine learning perspective, these cognitive behaviors act as structured inductive biases over the space of candidate features generated by the model. These behaviors have been exploited with success in ML models, and include backward chaining from outcomes, subgoal decomposition, verification against observability and leakage criteria, and explicit backtracking of rejected reasoning paths. In a controlled comparison, we show that enforcing cognitive behaviors yields features with higher empirical predictability than those under unconstrained vanilla LLM prompts. CoFEE achieves an average Success Rate Score that is 15.2% higher than the vanilla approach, while generating 29% fewer features and reducing costs by 53.3%. Using held-out feature evaluation, we assess whether cognitively induced features generalize beyond the data used for discovery. Our results indicate that, in our evaluated setting, reasoning control is associated with improvements in quality and efficiency of LLM-based feature discovery.
James Hipperson, Jonathan Hargreaves, Trevor Cox
Engineering structures are increasingly designed using numerical optimisation. However, traditional optimisation methods can be challenging with multiple objectives and many parameters. In machine learning, stable training of artificial neural networks with millions or billions of parameters is achieved using automatic differentiation frameworks such as JAX and Pytorch. Because these frameworks provide accelerated numerical linear algebra with automatic gradient tracking, they also enable differentiable implementations of numerical methods to be built. This facilitates faster gradient-based optimisation of geometry and materials, as well as solution of inverse problems. We demonstrate JAX-BEM, a differentiable Boundary Element Method (BEM) solver, showing that it matches the error of existing BEM codes for a benchmark problem and enables gradient-based geometry optimisation. Although the demonstrated examples are for acoustic simulations, the concept could be readily extended to electromagnetic waves.
Donggyu Lee, Hyeok Yun, Jungwon Kim, Junsik Min, Sungwon Park, Sangyoon Park, Jihee Kim
Do large language models (LLMs) exhibit systematic ideological bias when reasoning about economic causal effects? As LLMs are increasingly used in policy analysis and economic reporting, where directionally correct causal judgments are essential, this question has direct practical stakes. We present a systematic evaluation by extending the EconCausal benchmark with ideology-contested cases - instances where intervention-oriented (pro-government) and market-oriented (pro-market) perspectives predict divergent causal signs. From 10,490 causal triplets (treatment-outcome pairs with empirically verified effect directions) derived from top-tier economics and finance journals, we identify 1,056 ideology-contested instances and evaluate 20 state-of-the-art LLMs on their ability to predict empirically supported causal directions. We find that ideology-contested items are consistently harder than non-contested ones, and that across 18 of 20 models, accuracy is systematically higher when the empirically verified causal sign aligns with intervention-oriented expectations than with market-oriented ones. Moreover, when models err, their incorrect predictions disproportionately lean intervention-oriented, and this directional skew is not eliminated by one-shot in-context prompting. These results highlight that LLMs are not only less accurate on ideologically contested economic questions, but systematically less reliable in one ideological direction than the other, underscoring the need for direction-aware evaluation in high-stakes economic and policy settings.
Amir Noorizadegan, Sifan Wang
The Gaussian scale parameter \(ε\) is central to the behavior of Gaussian Kolmogorov--Arnold Networks (KANs), yet its role in deep edge-based architectures has not been studied systematically. In this paper, we investigate how \(ε\) affects Gaussian KANs through first-layer feature geometry, conditioning, and approximation behavior. Our central observation is that scale selection is governed primarily by the first layer, since it is the only layer constructed directly on the input domain and any loss of distinguishability introduced there cannot be recovered by later layers. From this viewpoint, we analyze the first-layer feature matrix and identify a practical operating interval, \[ ε\in \left[\frac{1}{G-1},\frac{2}{G-1}\right], \] where \(G\) denotes the number of Gaussian centers. For the standard shared-center Gaussian KAN used in current practice, we interpret this interval not as a universal optimality result, but as a stable and effective design rule, and validate it through brute-force sweeps over \(ε\) across function-approximation problems with different collocation densities, grid resolutions, network architectures, and input dimensions, as well as a physics-informed Helmholtz problem. We further show that this range is useful for fixed-scale selection, variable-scale constructions, constrained training of \(ε\), and efficient scale search using early training MSE. Finally, using a matched Chebyshev reference, we show that a properly scaled Gaussian KAN can already be competitive in accuracy relative to another standard KAN basis. In this way, the paper positions scale selection as a practical design principle for Gaussian KANs rather than as an ad hoc hyperparameter choice.
Jinliang Xu
The rapid collapse of decentralized game economies, often characterized by the \textit{death spiral,} remains the most formidable barrier to the mass adoption of Web3 gaming. This paper proposes that the sustainability of an open game economy is predicated on three necessary and sufficient conditions: Anti-Sybil Resilience, Anti-Capital Dominance, and Anti-Inflationary Saturation. The first section establishes a theoretical proof of these conditions, arguing that the absence of any single dimension leads to systemic failure. The second section explores the dialectical relationship between these dimensions, illustrating how unchecked automation and capital-driven monopolies accelerate asset hyperinflation. In the third section, we introduce the Identity-Bound Asset Integrity Model (IBAIM) as a comprehensive technical solution. IBAIM utilizes Zero-Knowledge (ZK) biometric hashing and Account Abstraction (AA) to anchor asset utility to unique human identities through a privacy-preserving and regulatory-compliant architecture. By exogenizing biometric verification to trusted local environments and utilizing Zero-Knowledge Proofs of Identity (zk-PoI), the model ensures absolute user privacy. Furthermore, by implementing an Asymmetric Utility Decay (AUD) engine-whereby assets suffer a vertical 50% utility cliff upon secondary transfer-and an entropy-driven thermodynamic degradation mechanism., the model successfully decouples financial speculation from in-game merit. Finally, we apply this framework to analyze prominent historical failures in the GameFi sector, demonstrating that their collapse was an inevitable consequence of violating these core economic constraints. Our findings suggest that trading a degree of asset liquidity for system integrity is the only viable path toward long-term economic viability in decentralized virtual worlds.
Seongmin Kim, Vincent R. Pascuzzi, Travis S. Humble, Thomas Beck, Sanghyo Hwang, Tengfei Luo, Eungkyu Lee, In-Saeng Suh
Apr 22, 2026·quant-ph·PDF Many real-world problems are naturally formulated as higher-order optimization (HUBO) tasks involving dense, multi-variable interactions, which are challenging to solve with classical methods. Quantum optimization offers a promising route, but hardware constraints and limitations to quadratic formulations have hampered their practicality. Here, we develop a distributed quantum optimization framework (DQOF) for dense, large-scale HUBO problems. DQOF assigns quantum circuits a central role in directly capturing higher-order interactions, while high-performance computing orchestrates large-scale parallelism and coordination. A clustering strategy enables wide quantum circuits without increasing depth, allowing efficient execution on near-term quantum hardware. We demonstrate high-quality solutions for HUBOs up to 500 variables within 170 seconds, significantly outperforming conventional approaches in solution quality and scalability. Applied to optical metamaterial design, DQOF efficiently discovers high-performance structures and shows that higher-order interactions are important for practical optimization problems. These results establish DQOF as a practical and scalable computational paradigm for large-scale scientific optimization.
Idoia Cortes Garcia, Peter F. Förster, Lennart Jansen, Wil Schilders, Sebastian Schöps
We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sources, which play a crucial role in engineering design workflows. Furthermore, the proof is constructive and provides a graph-based algorithmic framework for the computation of the decoupling, enabling its application to a variety of industry problems. These include the generation of consistent initial conditions, model order reduction, (scientific) machine learning, as well as speeding up conventional circuit simulation. In addition, the decoupling preserves the structure of MNA, i.e. the resulting systems remain sparse and key parts remain positive definite. We illustrate the decoupling using multiple examples, including some of the most common subcircuits containing controlled sources. Lastly, we also provide a first software implementation of the decoupling.
Hyeokmin Lee, Youngkyu Kim, Byounghyun Yoo
The advent of NMT has expanded the scope of translation beyond isolated sentences, enabling context to be preserved across paragraphs and documents. However, current evaluation metrics largely remain restricted to the sentence level and typically depend on reference translations. Without references, existing metrics cannot provide a clear basis for their quality assessments. To address these limitations, we propose an evaluation framework that independently extracts and compares latent topic structures within source and translated texts. This framework utilises various topic modelling techniques, including LSA, LDA and BERTopic, to achieve this. Our methodology captures statistical frequency information and semantic context, providing a comprehensive evaluation of the entire document. It aligns key topic tokens across languages using a bilingual dictionary and quantifies thematic consistency via cosine similarity. This allows us to evaluate how faithfully the translation maintains the thematic integrity of the source text, even in the absence of reference translations. To this end, we used a large scale dataset of 9.38 million Korean to English sentence pairs from AI Hub, which includes pre evaluated BLEU scores. We also calculated CometKiwi, a state of the art, reference free metric for this dataset, in order to conduct a comparative analysis with our proposed, topic based framework. Through this analysis, we confirmed that, unlike existing metrics, our framework evaluates the differentiated attribute of document level thematic units. Furthermore, visualising the key tokens that underpin the quantitative evaluation score provides clear insight into translation quality. Consequently, this study contributes to effectively complementing the existing translation evaluation system by proposing a new metric that intuitively identifies whether the document's theme has been preserved.
Kosuke Nakanishi, Hiroshi Yano, Yuki Sato
Apr 22, 2026·quant-ph·PDF We present an explicit quantum circuit construction for Hamiltonian simulation of a first-order velocity--stress formulation of the three-dimensional elastic wave equation in homogeneous isotropic media. Previous studies have shown how elastic wave equations can be cast into forms amenable to Hamiltonian simulation, but they typically rely on black box Hamiltonian access assumptions, making gate complexity estimation difficult. Starting from the first-order velocity--stress formulation, we discretize the system by finite differences, transform it into Schrödinger form, and exploit the separation between the component register and the spatial register to decompose the Hamiltonian into structured tensor product terms. This yields explicit implementations of first-order and second-order Trotter formulas for the resulting time evolution operator. We derive corresponding error bounds and constant sensitive qubit and CNOT complexity estimates in terms of the discretization parameter, simulation time, target accuracy, and material parameters. Numerical experiments validate the proposed framework through comparisons with the exact time evolution and reconstructed physical fields.
Pagkratis Tagkopoulos, Dimitris Sfondilis, Ilias Tagkopoulos, Tarek Zohdi
The prediction of sensory attributes from ingredient-level formulations is an emerging challenge at the intersection of food science and artificial intelligence. We address the fundamental question of whether the taste of a food can be predicted from its ingredients by treating recipes as composite materials. We apply Hashin--Shtrikman (HS) and Reuss--Voigt (RV) bounds, techniques originally developed for elastic moduli, to predict five taste dimensions (sweetness, sourness, bitterness, umami, saltiness) on a curated dataset of 70 recipes decomposed into 209 ingredient-level taste references with trained-panel ground truth. The bounds provided an additive baseline but systematically under-predict perceived taste: 77\% of actual taste values exceeded the HS upper bound, with the exceedance rate ranging from 26\% (bitterness) to 97\% (saltiness). We traced this gap to specific processing chemistry (Maillard reactions, caramelization, evaporative concentration, protein hydrolysis, and nucleotide synergy) and introduced a hybrid model that augments the HS baseline with eight chemistry-proxy features encoding these mechanisms. Our results show that our interpretable hybrid model eliminates the systematic bias and reduces mean absolute error by 27--62\% for sweetness, sourness, umami, and saltiness while using only 10 interpretable features, achieving performance comparable to a black-box Lasso regression on 115 per-ingredient features. We further demonstrate constrained inverse design via Differential Evolution, recovering ingredient formulations that match target taste profiles subject to compositional bounds.
Sadra Sabouri, Zeinabsadat Saghi, Run Huang, Sujay Maladi, Esmeralda Eufracio, Sumit Gulwani, Souti Chattopadhyay
Advances in AI agent capabilities have outpaced users' ability to meaningfully oversee their execution. AI agents can perform sophisticated, multi-step knowledge work autonomously from start to finish, yet this process remains effectively inaccessible during execution, often buried within large volumes of intermediate reasoning and outputs: by the time users receive the output, all underlying decisions have already been made without their involvement. This lack of transparency leaves users unable to examine the agent's assumptions, identify errors before they propagate, or redirect execution when it deviates from their intent. The stakes are particularly high in spreadsheet environments, where process and artifact are inseparable. Each decision the agent makes is recorded directly in cells that belong to and reflect on the user. We introduce Pista, a spreadsheet AI agent that decomposes execution into auditable, controllable actions, providing users with visibility into the agent's decision-making process and the capacity to intervene at each step. A formative study (N = 8) and a within-subjects summative evaluation (N = 16) comparing Pista to a baseline agent demonstrated that active participation in execution influenced not only task outcomes but also users' comprehension of the task, their perception of the agent, and their sense of role within the workflow. Users identified their own intent reflected in the agent's actions, detected errors that post-hoc review would have failed to surface, and reported a sense of co-ownership over the resulting output. These findings indicate that meaningful human oversight of AI agents in knowledge work requires not improved post-hoc review mechanisms, but active participation in decisions as they are made.
Sophia Zorek, Kushal Vyas, Yuhao Liu, David Lenz, Tom Peterka, Guha Balakrishnan
Neural fields, also known as implicit neural representations (INRs), offer a powerful framework for modeling continuous geometry, but their effectiveness in high-dimensional scientific settings is limited by slow convergence and scaling challenges. In this study, we extend INR models to handle spatiotemporal and multivariate signals and show how INR features can be transferred across scientific signals to enable efficient and scalable representation across time and ensemble runs in an amortized fashion. Across controlled transformation regimes (e.g., geometric transformations and localized perturbations of synthetic fields) and high-fidelity scientific domains-including turbulent flows, fluid-material impact dynamics, and astrophysical systems-we show that transferable features improve not only signal fidelity but also the accuracy of derived geometric and physical quantities, including density gradients and vorticity. In particular, transferable features reduce iterations to reach target reconstruction quality by up to an order of magnitude, increase early-stage reconstruction quality by multiple dB (with gains exceeding 10 dB in some cases), and consistently improve gradient-based physical accuracy.
Anton Kolonin, Alexey Glushchenko, Evgeny Bochkov, Abhishek Saxena
Evaluating the reasoning capabilities of Large Language Models (LLMs) for complex, quantitative financial tasks is a critical and unsolved challenge. Standard benchmarks often fail to isolate an agent's core ability to parse queries and orchestrate computations. To address this, we introduce a novel evaluation methodology and benchmark designed to rigorously measure an LLM agent's reasoning for financial time-series analysis. We apply this methodology in a large-scale empirical study using our framework, Time Series Augmented Generation (TSAG), where an LLM agent delegates quantitative tasks to verifiable, external tools. Our benchmark, consisting of 100 financial questions, is used to compare multiple SOTA agents (e.g., GPT-4o, Llama 3, Qwen2) on metrics assessing tool selection accuracy, faithfulness, and hallucination. The results demonstrate that capable agents can achieve near-perfect tool-use accuracy with minimal hallucination, validating the tool-augmented paradigm. Our primary contribution is this evaluation framework and the corresponding empirical insights into agent performance, which we release publicly to foster standardized research on reliable financial AI.
Akash Yadav, Taiwo A. Adebiyi, Ruda Zhang
Transformer-based scientific foundation models are increasingly deployed in high-stakes settings, but current architectures give deterministic outputs and provide limited support for calibrated predictive uncertainty. We propose Stochastic Attention, a lightweight inference-time modification that randomizes attention by replacing softmax weights with normalized multinomial samples controlled by a single concentration parameter, and produces predictive ensembles without retraining. To set this parameter, we introduce a calibration objective that matches the stochastic attention output with the target, yielding an efficient univariate post-hoc tuning problem. We evaluate this mechanism on two scientific foundation models for weather and timeseries forecasting along with an additional regression task. Across benchmarks against uncertainty-aware baselines, we find that Stochastic Attention achieves the strongest native calibration and the sharpest prediction intervals at comparable coverage, while requiring only minutes of post-hoc tuning versus days of retraining for competitive baselines.
Juliusz Wasieleski, Tomasz Służalec, Maciej Woźniak, Marcin Łoś, Andres Medina, Paulina Sepulveda, Albert Oliver Serra, Eirik Valseth, Anna Paszyńska, Maciej Paszyński
We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equations, we develop quasi-implicit time integration schemes using direction splitting of the differential operators. We use the Peaceman-Rachford and Strang splitting methods, including the Crank-Nicolson method. Based on these discretizations, we derive variational formulations and explore the Kronecker product structure of the matrices. In the wildfire model, there are some non-linear terms that we treat explicitly. We perform a detailed analysis of how treating these terms affects the stability of the time integration scheme. Namely, we show that a quasi-implicit time integration scheme achieves 10 times higher simulation accuracy. We present two wildfire simulations. The first is a simulation of the 2024 wildfire disaster in the Valparaíso region of Chile. The second one is a simulation of the 2019 wildfire disaster in Las Palmas de Gran Canaria, Spain. We discuss the numerical results and compare them against satellite images and measurement records. We also present a numerical experiment for comparison with the state-of-the-art wildfire simulation model FARSITE. Our sequential code has a linear computational cost of ${\cal O}(N)$. We also present the parallel scalability of the WILDFIRE-IGA-ADS code to illustrate the possibility of running the code on a local workstation.
Huayu Deng, Jinghui Zhong, Xiangming Zhu, Yunbo Wang, Xiaokang Yang
High-fidelity measurements of continuum physical fields are essential for scientific discovery and engineering design but remain challenging under sparse and constrained sensing. Conventional reconstruction methods typically rely on fixed sensor layouts, which cannot adapt to evolving physical states. We propose LASER, a unified, closed-loop framework that formulates active sensing as a Partially Observable Markov Decision Process (POMDP). At its core, LASER employs a continuum field latent world model that captures the underlying physical dynamics and provides intrinsic reward feedback. This enables a reinforcement learning policy to simulate ''what-if'' sensing scenarios within a latent imagination space. By conditioning sensor movements on predicted latent states, LASER navigates toward potentially high-information regions beyond current observations. Our experiments demonstrate that LASER consistently outperforms static and offline-optimized strategies, achieving high-fidelity reconstruction under sparsity across diverse continuum fields.
Luca Pennati, Stefano Markidis
Matrix-multiply-accumulate (MMA) units, or tensor cores, are now widespread across modern computing architectures. Yet, their use for particle-grid operators remains limited. In implicit particle methods, mass-matrix assembly is a reduction-dominated kernel in which weighted outer products of interpolation weights are accumulated over particle support. We show that this operation can be reformulated exactly, cell by cell, as a sequence of matrix products matched to hardware MMA tiles. The formulation is general with respect to interpolation order and hardware platform, and applies to both scalar mass matrices and the tensorial block mass matrix arising in implicit in the Energy-Conserving Semi-Implicit Method (ECSIM) for Particle-in-Cell simulations. We introduce particle batching and a support-group decomposition for higher-order shape functions whose stencil extends beyond a single cell, specialize the method to first- and second-order B-spline interpolation, and implement it on NVIDIA tensor cores. The resulting kernels achieve up to 3x over optimized conventional implementations and reduce end-to-end ECSIM runtime by 15%.