Model Reduction and Neural Networks

Derniers papiers

• Variational Neural Networks for Observable Thermodynamics (V-NOTS)

  Christopher Eldred, Fran\c{c}ois Gay-Balmaz, Vakhtang Putkaradze · 24 mars 2026

  Much attention has recently been devoted to data-based computing of evolution of physical systems. In such approaches, information about data points from past trajectories in phase space is used to reconstruct the equations of motion and to predict future solutions that have not been observed before…

• GAS: Improving Discretization of Diffusion ODEs via Generalized Adversarial Solver

  Aleksandr Oganov, Ilya Bykov, Eva Neudachina, Mishan Aliev, Alexander Tolmachev, Alexander Sidorov, Aleksandr Zuev, Andrey Okhotin, Denis Rakitin, Aibek Alanov · 24 mars 2026

  While diffusion models achieve state-of-the-art generation quality, they still suffer from computationally expensive sampling. Recent works address this issue with gradient-based optimization methods that distill a few-step ODE diffusion solver from the full sampling process, reducing the number of …

• SLE-FNO: Single-Layer Extensions for Task-Agnostic Continual Learning in Fourier Neural Operators

  Mahmoud Elhadidy, Roshan M. D'Souza, Amirhossein Arzani · 24 mars 2026

  Scientific machine learning is increasingly used to build surrogate models, yet most models are trained under a restrictive assumption in which future data follow the same distribution as the training set. In practice, new experimental conditions or simulation regimes may differ significantly, requi…

• CFNN: Continued Fraction Neural Network

  Chao Wang, Xuancheng Zhou, Ruilin Hou, Xiaoyu Cheng, Ruiyi Ding · 24 mars 2026

  Accurately characterizing non-linear functional manifolds with singularities is a fundamental challenge in scientific computing. While Multi-Layer Perceptrons (MLPs) dominate, their spectral bias hinders resolving high-curvature features without excessive parameters. We introduce Continued Fraction …

• Closed-form conditional diffusion models for data assimilation

  Brianna Binder, Assad Oberai · 24 mars 2026

  We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new samples from the data distribution by reversing a noise inje…

• SPINONet: Scalable Spiking Physics-informed Neural Operator for Computational Mechanics Applications

  Shailesh Garg, Luis Mandl, Somdatta Goswami, Souvik Chakraborty · 24 mars 2026

  Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where repeated operator evaluations in dense networks incur substa…

• Operator Learning for Smoothing and Forecasting

  Edoardo Calvello, Elizabeth Carlson, Nikola Kovachki, Michael N. Manta, Andrew M. Stuart · 24 mars 2026

  Machine learning has opened new frontiers in purely data-driven algorithms for data assimilation in, and for forecasting of, dynamical systems; the resulting methods are showing some promise. However, in contrast to model-driven algorithms, analysis of these data-driven methods is poorly developed. …

• FRIREN: Beyond Trajectories -- A Spectral Lens on Time

  Qilin Wang · 24 mars 2026

  Long-term time-series forecasting (LTSF) models are often presented as general-purpose solutions that can be applied across domains, implicitly assuming that all data is pointwise predictable. Using chaotic systems such as Lorenz-63 as a case study, we argue that geometric structure - not pointwise …

• Generalization Limits of In-Context Operator Networks for Higher-Order Partial Differential Equations

  Jamie Mahowald, Tan Bui-Thanh · 24 mars 2026

  We investigate the generalization capabilities of In-Context Operator Networks (ICONs), a new class of operator networks that build on the principles of in-context learning, for higher-order partial differential equations. We extend previous work by expanding the type and scope of differential equat…

• Quotient Geometry, Effective Curvature, and Implicit Bias in Simple Shallow Neural Networks

  Hang-Cheng Dong, Pengcheng Cheng · 24 mars 2026

  Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric quantities computed directly in the ambient Euclidean parameter sp…

• Goal-oriented learning of stochastic dynamical systems using error bounds on path-space observables

  Joanna Zou, Han Cheng Lie, Youssef Marzouk · 24 mars 2026

  The governing equations of stochastic dynamical systems often become cost-prohibitive for numerical simulation at large scales. Surrogate models of the governing equations, learned from data of the high-fidelity system, are routinely used to predict key observables with greater efficiency. However, …

• Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms

  Melissa Adrian, Daniel Sanz-Alonso, Rebecca Willett · 24 mars 2026

  Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics. This paper introduces a framework for jointly learning the stat…

• JointFM-0.1: A Foundation Model for Multi-Target Joint Distributional Prediction

  Stefan Hackmann · 24 mars 2026

  Despite the rapid advancements in Artificial Intelligence (AI), Stochastic Differential Equations (SDEs) remain the gold-standard formalism for modeling systems under uncertainty. However, applying SDEs in practice is fraught with challenges: modeling risk is high, calibration is often brittle, and …

• Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach

  Gianluca Fabiani, Michail E. Kavousanakis, Constantinos Siettos, Ioannis G. Kevrekidis · 24 mars 2026

  We address a numerical framework for the stability and bifurcation analysis of nonlinear partial differential equations (PDEs) in which the solution is sought in the function space spanned by physics-informed random projection neural networks (PI-RPNNs), and discretized via a collocation approach. T…

• Multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation overcome the curse of dimensionality when approximating semilinear parabolic partial differential equations in $L^p$-sense

  Ariel Neufeld, Tuan Anh Nguyen · 24 mars 2026

  We prove that multilevel Picard approximations and deep neural networks with ReLU, leaky ReLU, and softplus activation are capable of approximating solutions of semilinear Kolmogorov PDEs in $L^\mathfrak{p}$-sense, $\mathfrak{p}\in [2,\infty)$, in the case of gradient-independent, Lipschitz-continuo…

• Deep Neural Networks with General Activations: Super-Convergence in Sobolev Norms

  Yahong Yang, Juncai He · 24 mars 2026

  This paper establishes a comprehensive approximation result for deep fully-connected neural networks with commonly-used and general activation functions in Sobolev spaces $W^{n,\infty}$, with errors measured in the $W^{m,p}$-norm for $m < n$ and $1\le p \le \infty$. The derived rates surpass those o…

• SymCircuit: Bayesian Structure Inference for Tractable Probabilistic Circuits via Entropy-Regularized Reinforcement Learning

  Y. Sungtaek Ju · 24 mars 2026

  Probabilistic circuit (PC) structure learning is hampered by greedy algorithms that make irreversible, locally optimal decisions. We propose SymCircuit, which replaces greedy search with a learned generative policy trained via entropy-regularized reinforcement learning. Instantiating the RL-as-infer…

• FluidWorld: Reaction-Diffusion Dynamics as a Predictive Substrate for World Models

  Fabien Polly · 24 mars 2026

  World models learn to predict future states of an environment, enabling planning and mental simulation. Current approaches default to Transformer-based predictors operating in learned latent spaces. This comes at a cost: O(N^2) computation and no explicit spatial inductive bias. This paper asks a fo…

• CurvZO: Adaptive Curvature-Guided Sparse Zeroth-Order Optimization for Efficient LLM Fine-Tuning

  Shuo Wang, Ziyu Chen, Ming Tang · 24 mars 2026

  Fine-tuning large language models (LLMs) with backpropagation achieves high performance but incurs substantial memory overhead, limiting scalability on resource-constrained hardware. Zeroth-order (ZO) optimization provides a memory-efficient alternative by relying solely on forward passes, yet it ty…

• From Data to Laws: Neural Discovery of Conservation Laws Without False Positives

  Rahul D Ray · 24 mars 2026

  Conservation laws are fundamental to understanding dynamical systems, but discovering them from data remains challenging due to parameter variation, non-polynomial invariants, local minima, and false positives on chaotic systems. We introduce NGCG, a neural-symbolic pipeline that decouples dynamics …

• Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems

  Pantelis R. Vlachas, Konstantinos Vlachas, Eleni Chatzi · 24 mars 2026

  Dynamical systems play a key role in modeling, forecasting, and decision-making across a wide range of scientific domains. However, variations in system parameters, also referred to as parametric variability, can lead to drastically different model behavior and output, posing challenges for construc…

• An Adaptive Machine Learning Framework for Fluid Flow in Dual-Network Porous Media

  V. S. Maduri, K. B. Nakshatrala · 23 mars 2026

  Porous materials -- natural or engineered -- often exhibit dual pore-network structures that govern processes such as mineral exploration and hydrocarbon recovery from tight shales. Double porosity/permeability (DPP) mathematical models describe incompressible fluid flow through two interacting pore…

• Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations

  Jun Liu · 23 mars 2026

  Many core problems in nonlinear systems analysis and control can be recast as solving partial differential equations (PDEs) such as Lyapunov and Hamilton-Jacobi-Bellman (HJB) equations. Physics-informed neural networks (PINNs) have emerged as a promising mesh-free approach for approximating their so…

• MeanFlow Meets Control: Scaling Sampled-Data Control for Swarms

  Anqi Dong, Yongxin Chen, Karl H. Johansson, Johan Karlsson · 23 mars 2026

  Steering large-scale swarms in only a few control updates is challenging because real systems operate in sampled-data form: control inputs are updated intermittently and applied over finite intervals. In this regime, the natural object is not an instantaneous velocity field, but a finite-window cont…

• FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions

  Chloe H. Choi, Alison L. Marsden, Daniele E. Schiavazzi · 23 mars 2026

  Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of traini…