Model Reduction and Neural Networks

Derniers papiers

• Kinetic-based regularization: Learning spatial derivatives and PDE applications

  Abhisek Ganguly, Santosh Ansumali, Sauro Succi · 9 mars 2026

  Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression method with a single trainable parameter, to learn spatial d…

• Decoding Partial Differential Equations: Cross-Modal Adaptation of Decoder-only Models to PDEs

  Paloma Garc\'ia-de-Herreros, Philipp Slusallek, Dietrich Klakow, Vagrant Gautam · 9 mars 2026

  While large language models are primarily used on natural language tasks, they have also shown great promise when adapted to new modalities, e.g., for scientific machine learning tasks. Most proposed approaches for such cross-modal adaptation of language models focus on encoder-only transformer mode…

• JAWS: Enhancing Long-term Rollout of Neural Operators via Spatially-Adaptive Jacobian Regularization

  Fengxiang Nie, Yasuhiro Suzuki · 9 mars 2026

  Data-driven surrogate models improve the efficiency of simulating continuous dynamical systems, yet their autoregressive rollouts are often limited by instability and spectral blow-up. While global regularization techniques can enforce contractive dynamics, they uniformly damp high-frequency feature…

• FourierSpecNet: Neural Collision Operator Approximation Inspired by the Fourier Spectral Method for Solving the Boltzmann Equation

  Jae Yong Lee, Gwang Jae Jung, Byung Chan Lim, Hyung Ju Hwang · 9 mars 2026

  The Boltzmann equation, a fundamental model in kinetic theory, describes the evolution of particle distribution functions through a nonlinear, high-dimensional collision operator. However, its numerical solution remains computationally demanding, particularly for inelastic collisions and high-dimens…

• On the Value of Tokeniser Pretraining in Physics Foundation Models

  Hadi Sotoudeh, Payel Mukhopadhyay, Ruben Ohana, Michael McCabe, Neil D. Lawrence, Shirley Ho, Miles Cranmer · 9 mars 2026

  We investigate the impact of tokeniser pretraining on the accuracy and efficiency of physics emulation. Modern high-resolution simulations produce vast volumes of data spanning diverse physical regimes and scales. Training foundation models to learn the dynamics underlying such data enables the mode…

• Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs

  Akshay Govind Srinivasan, Balaji Srinivasan · 9 mars 2026

  Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times, Physics-Informed Extreme Learning Machines (PIELMs) offer a r…

• Certified and accurate computation of function space norms of deep neural networks

  Johannes Gr\"undler, Moritz Maibaum, Philipp Petersen · 9 mars 2026

  Neural network methods for PDEs require reliable error control in function space norms. However, trained neural networks can typically only be probed at a finite number of point values. Without strong assumptions, point evaluations alone do not provide enough information to derive tight deterministi…

• Towards Efficient and Stable Ocean State Forecasting: A Continuous-Time Koopman Approach

  Rares Grozavescu, Pengyu Zhang, Mark Girolami, Etienne Meunier · 9 mars 2026

  We investigate the Continuous-Time Koopman Autoencoder (CT-KAE) as a lightweight surrogate model for long-horizon ocean state forecasting in a two-layer quasi-geostrophic (QG) system. By projecting nonlinear dynamics into a latent space governed by a linear ordinary differential equation, the model …

• Frequency-Separable Hamiltonian Neural Network for Multi-Timescale Dynamics

  Yaojun Li, Yulong Yang, Christine Allen-Blanchette · 9 mars 2026

  While Hamiltonian mechanics provides a powerful inductive bias for neural networks modeling dynamical systems, Hamiltonian Neural Networks and their variants often fail to capture complex temporal dynamics spanning multiple timescales. This limitation is commonly linked to the spectral bias of deep …

• Merging Memory and Space: A State Space Neural Operator

  Nodens Koren, Samuel Lanthaler · 9 mars 2026

  We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint spatiotemporal modeling, introducing two key mechanisms: *adapti…

• Structured Kolmogorov-Arnold Neural ODEs for Interpretable Learning and Symbolic Discovery of Nonlinear Dynamics

  Wei Liu, Kiran Bacsa, Loon Ching Tang, Eleni Chatzi · 6 mars 2026

  Understanding and modeling nonlinear dynamical systems is a fundamental challenge across science and engineering. Deep learning has shown remarkable potential for capturing complex system behavior, yet achieving models that are both accurate and physically interpretable remains difficult. To address…

• Flowers: A Warp Drive for Neural PDE Solvers

  Till Muser, Alexandra Spitzer, Matti Lassas, Maarten V. de Hoop, Ivan Dokmani\'c · 6 mars 2026

  We introduce Flowers, a neural architecture for learning PDE solution operators built entirely from multihead warps. Aside from pointwise channel mixing and a multiscale scaffold, Flowers use no Fourier multipliers, no dot-product attention, and no convolutional mixing. Each head predicts a displace…

• Overtone: Cyclic Patch Modulation for Clean, Efficient, and Flexible Physics Emulators

  Payel Mukhopadhyay, Michael McCabe, Ruben Ohana, Miles Cranmer · 6 mars 2026

  Transformer-based PDE surrogates achieve remarkable performance but face two key challenges: fixed patch sizes cause systematic error accumulation at harmonic frequencies, and computational costs remain inflexible regardless of problem complexity or available resources. We introduce Overtone, a unif…

• Improving the accuracy of physics-informed neural networks via last-layer retraining

  Saad Qadeer, Panos Stinis · 6 mars 2026

  Physics-informed neural networks (PINNs) are a versatile tool in the burgeoning field of scientific machine learning for solving partial differential equations (PDEs). However, determining suitable training strategies for them is not obvious, with the result that they typically yield moderately accu…

• Particle-Guided Diffusion for Gas-Phase Reaction Kinetics

  Andrew Millard, Henrik Pedersen · 6 mars 2026

  Physics-guided sampling with diffusion model priors has shown promise for solving partial differential equation (PDE) governed problems, but applications to chemically meaningful reaction-transport systems remain limited. We apply diffusion-based guided sampling to gas-phase chemical reactions by tr…

• A physics-informed U-Net-LSTM network for nonlinear structural response under seismic excitation

  Sutirtha Biswas, Kshitij Kumar Yadav · 6 mars 2026

  Accurate and efficient seismic response prediction is essential for the design of resilient structures. While the Finite Element Method (FEM) remains the standard for nonlinear seismic analysis, its high computational demands limit its scalability and real-time applicability. Recent developments in …

• Uncertainty-Calibrated Spatiotemporal Field Diffusion with Sparse Supervision

  Kevin Valencia, Xihaier Luo, Shinjae Yoo, David Keetae Park · 6 mars 2026

  Physical fields are typically observed only at sparse, time-varying sensor locations, making forecasting and reconstruction ill-posed and uncertainty-critical. We present SOLID, a mask-conditioned diffusion framework that learns spatiotemporal dynamics from sparse observations alone: training and ev…

• Towards a data-scale independent regulariser for robust sparse identification of non-linear dynamics

  Jay Raut, Daniel N. Wilke, Stephan Schmidt · 6 mars 2026

  Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is particularly acute for the Sparse Identification of Nonlinear Dynamics …

• Multilevel Training for Kolmogorov Arnold Networks

  Ben S. Southworth, Jonas A. Actor, Graham Harper, Eric C. Cyr · 6 mars 2026

  Algorithmic speedup of training common neural architectures is made difficult by the lack of structure guaranteed by the function compositions inherent to such networks. In contrast to multilayer perceptrons (MLPs), Kolmogorov-Arnold networks (KANs) provide more structure by expanding learned activa…

• FastLSQ: A Framework for One-Shot PDE Solving

  Antonin Sulc · 5 mars 2026

  We present FastLSQ, a framework for fast PDE solving and inverse problems built on sinusoidal random Fourier features with exact analytical derivatives. Sinusoids are eigenfunctions of differentiation: derivatives of any order admit closed-form evaluation in $O(1)$ operations, enabling graph-free op…

• LUMINA: Foundation Models for Topology Transferable ACOPF

  Yijiang Li, Zeeshan Memon, Hongwei Jin, Stefano Fenu, Keunju Song, Sunash B Sharma, Parfait Gasana, Hongseok Kim, Liang Zhao, Kibaek Kim · 5 mars 2026

  Foundation models in general promise to accelerate scientific computation by learning reusable representations across problem instances, yet constrained scientific systems, where predictions must satisfy physical laws and safety limits, pose unique challenges that stress conventional training paradi…

• Extending Neural Operators: Robust Handling of Functions Beyond the Training Set

  Blaine Quackenbush, Paul J. Atzberger · 5 mars 2026

  We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of Reproducing Kernel Hilbert Spaces (RKHSs). We provide theorems …

• Error as Signal: Stiffness-Aware Diffusion Sampling via Embedded Runge-Kutta Guidance

  Inho Kong, Sojin Lee, Youngjoon Hong, Hyunwoo J. Kim · 5 mars 2026

  Classifier-Free Guidance (CFG) has established the foundation for guidance mechanisms in diffusion models, showing that well-designed guidance proxies significantly improve conditional generation and sample quality. Autoguidance (AG) has extended this idea, but it relies on an auxiliary network and …

• Continuous Modal Logical Neural Networks: Modal Reasoning via Stochastic Accessibility

  Antonin Sulc · 5 mars 2026

  We propose Fluid Logic, a paradigm in which modal logical reasoning, temporal, epistemic, doxastic, deontic, is lifted from discrete Kripke structures to continuous manifolds via Neural Stochastic Differential Equations (Neural SDEs). Each type of modal operator is backed by a dedicated Neural SDE, …

• Hierarchical Inference and Closure Learning via Adaptive Surrogates for ODEs and PDEs

  Pengyu Zhang, Arnaud Vadeboncoeur, Alex Glyn-Davies, Mark Girolami · 5 mars 2026

  Inverse problems are the task of calibrating models to match data. They play a pivotal role in diverse engineering applications by allowing practitioners to align models with reality. In many applications, engineers and scientists do not have a complete picture of i) the detailed properties of a sys…