Model Reduction and Neural Networks

Derniers papiers

• Avoiding Premature Collapse: Adaptive Annealing for Entropy-Regularized Structural Inference

  Yizhi Liu · 2 février 2026

  Differentiable matching layers, often implemented via entropy-regularized Optimal Transport, serve as a critical approximate inference mechanism in structural prediction. However, recovering discrete permutations via annealing $\epsilon \to 0$ is notoriously unstable. We identify a fundamental mecha…

• Thompson Sampling via Fine-Tuning of LLMs

  Nicolas Menet, Aleksandar Terzi\'c, Michael Hersche, Andreas Krause, Abbas Rahimi · 2 février 2026

  Bayesian optimization in large unstructured discrete spaces is often hindered by the computational cost of maximizing acquisition functions due to the absence of gradients. We propose a scalable alternative based on Thompson sampling that eliminates the need for acquisition function maximization by …

• MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics

  Mikel M. Iparraguirre, Iciar Alfaro, David Gonzalez, Elias Cueto · 2 février 2026

  We present MeshGraphNet-Transformer (MGN-T), a novel architecture that combines the global modeling capabilities of Transformers with the geometric inductive bias of MeshGraphNets, while preserving a mesh-based graph representation. MGN-T overcomes a key limitation of standard MGN, the inefficient l…

• Perplexity Cannot Always Tell Right from Wrong

  Petar Veli\v{c}kovi\'c, Federico Barbero, Christos Perivolaropoulos, Simon Osindero, Razvan Pascanu · 2 février 2026

  Perplexity -- a function measuring a model's overall level of "surprise" when encountering a particular output -- has gained significant traction in recent years, both as a loss function and as a simple-to-compute metric of model quality. Prior studies have pointed out several limitations of perplex…

• Particle-Guided Diffusion Models for Partial Differential Equations

  Andrew Millard, Fredrik Lindsten, Zheng Zhao · 2 février 2026

  We introduce a guided stochastic sampling method that augments sampling from diffusion models with physics-based guidance derived from partial differential equation (PDE) residuals and observational constraints, ensuring generated samples remain physically admissible. We embed this sampling procedur…

• Physics-Informed Neural Networks and Neural Operators for Parametric PDEs

  Zhuo Zhang, Xiong Xiong, Sen Zhang, Yuan Zhao, Xi Yang · 2 février 2026

  PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter space exploration prohibitively expensive. Recent machine learn…

• Discovering Scaling Exponents with Physics-Informed M\"untz-Sz\'asz Networks

  Gnankan Landry Regis N'guessan, Bum Jun Kim · 2 février 2026

  Physical systems near singularities, interfaces, and critical points exhibit power-law scaling, yet standard neural networks leave the governing exponents implicit. We introduce physics-informed M"untz-Sz'asz Networks (MSN-PINN), a power-law basis network that treats scaling exponents as trainable p…

• Benchmarking Long Roll-outs of Auto-regressive Neural Operators for the Compressible Navier-Stokes Equations with Conserved Quantity Correction

  Sean Current, Chandan Kumar, Datta Gaitonde, Srinivasan Parthasarathy · 2 février 2026

  Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have struggle to perform well over long prediction durations due…

• Knowledge-Informed Kernel State Reconstruction for Interpretable Dynamical System Discovery

  Luca Muscarnera, Silas Ruhrberg Est\'evez, Samuel Holt, Evgeny Saveliev, Mihaela van der Schaar · 2 février 2026

  Recovering governing equations from data is central to scientific discovery, yet existing methods often break down under noisy, partial observations, or rely on black-box latent dynamics that obscure mechanism. We introduce MAAT (Model Aware Approximation of Trajectories), a framework for symbolic d…

• Diffusion-based Annealed Boltzmann Generators : benefits, pitfalls and hopes

  Louis Grenioux, Maxence Noble · 30 janvier 2026

  Sampling configurations at thermodynamic equilibrium is a central challenge in statistical physics. Boltzmann Generators (BGs) tackle it by combining a generative model with a Monte Carlo (MC) correction step to obtain asymptotically unbiased samples from an unnormalized target. Most current BGs use…

• Conditional Denoising Model as a Physical Surrogate Model

  Jos\'e Afonso, Pedro Viegas, Rodrigo Ventura, Vasco Guerra · 30 janvier 2026

  Surrogate modeling for complex physical systems typically faces a trade-off between data-fitting accuracy and physical consistency. Physics-consistent approaches typically treat physical laws as soft constraints within the loss function, a strategy that frequently fails to guarantee strict adherence…

• Learning to Advect: A Neural Semi-Lagrangian Architecture for Weather Forecasting

  Carlos A. Pereira, St\'ephane Gaudreault, Valentin Dallerit, Christopher Subich, Shoyon Panday, Siqi Wei, Sasa Zhang, Siddharth Rout, Eldad Haber, Raymond J. Spiteri, David Millard, Emilia Diaconescu · 30 janvier 2026

  Recent machine-learning approaches to weather forecasting often employ a monolithic architecture, where distinct physical mechanisms (advection, transport), diffusion-like mixing, thermodynamic processes, and forcing are represented implicitly within a single large network. This representation is pa…

• LLM4Fluid: Large Language Models as Generalizable Neural Solvers for Fluid Dynamics

  Qisong Xiao, Xinhai Chen, Qinglin Wang, Xiaowei Guo, Binglin Wang, Weifeng Chen, Zhichao Wang, Yunfei Liu, Rui Xia, Hang Zou, Gencheng Liu, Shuai Li, Jie Liu · 30 janvier 2026

  Deep learning has emerged as a promising paradigm for spatio-temporal modeling of fluid dynamics. However, existing approaches often suffer from limited generalization to unseen flow conditions and typically require retraining when applied to new scenarios. In this paper, we present LLM4Fluid, a spa…

• PILD: Physics-Informed Learning via Diffusion

  Tianyi Zeng, Tianyi Wang, Jiaru Zhang, Zimo Zeng, Feiyang Zhang, Yiming Xu, Sikai Chen, Yajie Zou, Yangyang Wang, Junfeng Jiao, Christian Claudel, Xinbo Chen · 30 janvier 2026

  Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in practical engineering and scientific problems where physical laws need to be followed. This paper proposes Physics-Informed Learning via Dif…

• Parametric Hyperbolic Conservation Laws: A Unified Framework for Conservation, Entropy Stability, and Hyperbolicity

  Lizuo Liu, Lu Zhang, Anne Gelb · 30 janvier 2026

  We propose a parametric hyperbolic conservation law (SymCLaw) for learning hyperbolic systems directly from data while ensuring conservation, entropy stability, and hyperbolicity by design. Unlike existing approaches that typically enforce only conservation or rely on prior knowledge of the governin…

• Fast and Geometrically Grounded Lorentz Neural Networks

  Robert van der Klis, Ricardo Ch\'avez Torres, Max van Spengler, Yuhui Ding, Thomas Hofmann, Pascal Mettes · 30 janvier 2026

  Hyperbolic space is quickly gaining traction as a promising geometry for hierarchical and robust representation learning. A core open challenge is the development of a mathematical formulation of hyperbolic neural networks that is both efficient and captures the key properties of hyperbolic space. T…

• Provably Reliable Classifier Guidance through Cross-entropy Error Control

  Sharan Sahu, Arisina Banerjee, Yuchen Wu · 30 janvier 2026

  Classifier-guided diffusion models generate conditional samples by augmenting the reverse-time score with the gradient of a learned classifier, yet it remains unclear whether standard classifier training procedures yield effective diffusion guidance. We address this gap by showing that, under mild s…

• Improving Classifier-Free Guidance of Flow Matching via Manifold Projection

  Jian-Feng Cai, Haixia Liu, Zhengyi Su, Chao Wang · 30 janvier 2026

  Classifier-free guidance (CFG) is a widely used technique for controllable generation in diffusion and flow-based models. Despite its empirical success, CFG relies on a heuristic linear extrapolation that is often sensitive to the guidance scale. In this work, we provide a principled interpretation …

• Predict-Project-Renoise: Sampling Diffusion Models under Hard Constraints

  Omer Rochman-Sharabi, Gilles Louppe · 30 janvier 2026

  Neural emulators based on diffusion models show promise for scientific applications, but vanilla models cannot guarantee physical accuracy or constraint satisfaction. We address this by introducing a constrained sampling framework that enforces hard constraints, such as physical laws or observationa…

• PHDME: Physics-Informed Diffusion Models without Explicit Governing Equations

  Kaiyuan Tan, Kendra Givens, Peilun Li, Thomas Beckers · 30 janvier 2026

  Diffusion models provide expressive priors for forecasting trajectories of dynamical systems, but are typically unreliable in the sparse data regime. Physics-informed machine learning (PIML) improves reliability in such settings; however, most methods require \emph{explicit governing equations} duri…

• MORPH: PDE Foundation Models with Arbitrary Data Modality

  Mahindra Singh Rautela, Alexander Most, Siddharth Mansingh, Bradley C. Love, Alexander Scheinker, Diane Oyen, Nathan Debardeleben, Earl Lawrence, Ayan Biswas · 30 janvier 2026

  We introduce MORPH, a modality-agnostic, autoregressive foundation model for partial differential equations (PDEs). MORPH is built on a convolutional vision transformer backbone that seamlessly handles heterogeneous spatiotemporal datasets of varying data modality (1D--3D) at different resolutions, …

• TINNs: Time-Induced Neural Networks for Solving Time-Dependent PDEs

  Chen-Yang Dai, Che-Chia Chang, Te-Sheng Lin, Ming-Chih Lai, Chieh-Hsin Lai · 29 janvier 2026

  Physics-informed neural networks (PINNs) solve time-dependent partial differential equations (PDEs) by learning a mesh-free, differentiable solution that can be evaluated anywhere in space and time. However, standard space--time PINNs take time as an input but reuse a single network with shared weig…

• An Empirical Investigation of Neural ODEs and Symbolic Regression for Dynamical Systems

  Panayiotis Ioannou, Pietro Li\`o, Pietro Cicuta · 29 janvier 2026

  Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we explore the extrapolation capabilities of Neural Ordinary Differen…

• Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines

  Yuxuan Bao, Jan Zajac, Megan Powers, Venkat Raman, J. Nathan Kutz · 29 janvier 2026

  Bridging the sim2real gap between computationally inexpensive models and complex physical systems remains a central challenge in machine learning applications to engineering problems, particularly in multi-scale settings where reduced-order models typically capture only dominant dynamics. In this wo…

• Loss Landscape Geometry and the Learning of Symmetries: Or, What Influence Functions Reveal About Robust Generalization

  James Amarel, Robyn Miller, Nicolas Hengartner, Benjamin Migliori, Emily Casleton, Alexei Skurikhin, Earl Lawrence, Gerd J. Kunde · 29 janvier 2026

  We study how neural emulators of partial differential equation solution operators internalize physical symmetries by introducing an influence-based diagnostic that measures the propagation of parameter updates between symmetry-related states, defined as the metric-weighted overlap of loss gradients …