Model Reduction and Neural Networks

Derniers papiers

• Informed Machine Learning with Knowledge Landmarks

  Chuyi Dai, Witold Pedrycz, Suping Xu, Ding Liu, Xianmin Wang · 2 avril 2026

  Informed Machine Learning has emerged as a viable generalization of Machine Learning (ML) by building a unified conceptual and algorithmic setting for constructing models on a unified basis of knowledge and data. Physics-informed ML involving physics equations is one of the developments within Infor…

• Phase space integrity in neural network models of Hamiltonian dynamics: A Lagrangian descriptor approach

  Abrari Noor Hasmi, Haralampos Hatzikirou, Hadi Susanto · 2 avril 2026

  We propose Lagrangian Descriptors (LDs) as a diagnostic framework for evaluating neural network models of Hamiltonian systems beyond conventional trajectory-based metrics. Standard error measures quantify short-term predictive accuracy but provide little insight into global geometric structures such…

• Lie Generator Networks for Nonlinear Partial Differential Equations

  Shafayeth Jamil, Rehan Kapadia · 2 avril 2026

  Linear dynamical systems are fully characterized by their eigenspectra, accessible directly from the generator of the dynamics. For nonlinear systems governed by partial differential equations, no equivalent theory exists. We introduce Lie Generator Network-Koopman (LGN-KM), a neural operator that l…

• LAtent Phase Inference from Short time sequences using SHallow REcurrent Decoders (LAPIS-SHRED)

  Yuxuan Bao, Xingyue Zhang, J. Nathan Kutz · 2 avril 2026

  Reconstructing full spatio-temporal dynamics from sparse observations in both space and time remains a central challenge in complex systems, as measurements can be spatially incomplete and can be also limited to narrow temporal windows. Yet approximating the complete spatio-temporal trajectory is es…

• SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Sampling

  Stepan Tretiakov, Xingjian Li, Krishna Kumar · 2 avril 2026

  Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assumption limits applicability to problems with variable sensor layouts, missing data, point sources, and sample-based repres…

• Hybrid Energy-Based Models for Physical AI: Provably Stable Identification of Port-Hamiltonian Dynamics

  Simone Betteti, Luca Laurenti · 2 avril 2026

  Energy-based models (EBMs) implement inference as gradient descent on a learned Lyapunov function, yielding interpretable, structure-preserving alternatives to black-box neural ODEs and aligning naturally with physical AI. Yet their use in system identification remains limited, and existing architec…

• Predicting Wave Reflection and Transmission in Heterogeneous Media via Fourier Operator-Based Transformer Modeling

  Zhe Bai, Hans Johansen · 2 avril 2026

  We develop a machine learning (ML) surrogate model to approximate solutions to Maxwell's equations in one dimension, focusing on scenarios involving a material interface that reflects and transmits electro-magnetic waves. Derived from high-fidelity Finite Volume (FV) simulations, our training data i…

• Data-Driven Reachability Analysis via Diffusion Models with PAC Guarantees

  Yanliang Huang, Peng Xie, Wenyuan Wu, Zhuoqi Zeng, Amr Alanwar · 2 avril 2026

  We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from trajectory data alone. The predicted reachable set takes the f…

• Performance of Neural and Polynomial Operator Surrogates

  Josephine Westermann, Benno Huber, Thomas O'Leary-Roseberry, Jakob Zech · 2 avril 2026

  We consider the problem of constructing surrogate operators for parameter-to-solution maps arising from parametric partial differential equations, where repeated forward model evaluations are computationally expensive. We present a systematic empirical comparison of neural operator surrogates, inclu…

• FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles

  Ziwei Li, Yuhan Duan, Tianyu Xiong, Yi-Tang Chen, Wei-Lun Chao, Han-Wei Shen · 1 avril 2026

  Surrogate models are essential for efficient exploration of large-scale ensemble simulations. Implicit neural representations (INRs) provide a compact and continuous framework for modeling spatially structured data, but they often struggle with learning complex localized structures within the scient…

• Derived Fields Preserve Fine-Scale Detail in Budgeted Neural Simulators

  Wenshuo Wang, Fan Zhang · 1 avril 2026

  Fine-scale-faithful neural simulation under fixed storage budgets remains challenging. Many existing methods reduce high-frequency error by improving architectures, training objectives, or rollout strategies. However, under budgeted coarsen-quantize-decode pipelines, fine detail can already be lost …

• Beta-Scheduling: Momentum from Critical Damping as a Diagnostic and Correction Tool for Neural Network Training

  Ivan Pasichnyk · 1 avril 2026

  Standard neural network training uses constant momentum (typically 0.9), a convention dating to 1964 with limited theoretical justification for its optimality. We derive a time-varying momentum schedule from the critically damped harmonic oscillator: mu(t) = 1 - 2*sqrt(alpha(t)), where alpha(t) is…

• Interpretable Physics Extraction from Data for Linear Dynamical Systems using Lie Generator Networks

  Shafayeth Jamil, Rehan Kapadia · 31 mars 2026

  When the system is linear, why should learning be nonlinear? Linear dynamical systems, the analytical backbone of control theory, signal processing and circuit analysis, have exact closed-form solutions via the state transition matrix. Yet when system parameters must be inferred from data, recent ne…

• Koopman-based surrogate modeling for reinforcement-learning-control of Rayleigh-Benard convection

  Tim Plotzki, Sebastian Peitz · 31 mars 2026

  Training reinforcement learning (RL) agents to control fluid dynamics systems is computationally expensive due to the high cost of direct numerical simulations (DNS) of the governing equations. Surrogate models offer a promising alternative by approximating the dynamics at a fraction of the computat…

• SIMR-NO: A Spectrally-Informed Multi-Resolution Neural Operator for Turbulent Flow Super-Resolution

  Muhammad Abid, Omer San · 31 mars 2026

  Reconstructing high-resolution turbulent flow fields from severely under-resolved observations is a fundamental inverse problem in computational fluid dynamics and scientific machine learning. Classical interpolation methods fail to recover missing fine-scale structures, while existing deep learning…

• Comparing Physics-Informed and Neural ODE Approaches for Modeling Nonlinear Biological Systems: A Case Study Based on the Morris-Lecar Model

  Nikolaos M. Matzakos, Chrisovalantis Sfyrakis · 31 mars 2026

  Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs) represent two distinct machine learning frameworks for modeling nonlinear neuronal dynamics. This study systematically evaluates their performance on the two-dimensional Morris-Lecar model across three canoni…

• Physics-Guided Transformer (PGT): Physics-Aware Attention Mechanism for PINNs

  Ehsan Zeraatkar, Rodion Podorozhny, Jelena Te\v{s}i\'c · 31 mars 2026

  Reconstructing continuous physical fields from sparse, irregular observations is a central challenge in scientific machine learning, particularly for systems governed by partial differential equations (PDEs). Existing physics-informed methods typically enforce governing equations as soft penalty ter…

• A Comparative Investigation of Thermodynamic Structure-Informed Neural Networks

  Guojie Li, Liu Hong · 31 mars 2026

  Physics-informed neural networks (PINNs) offer a unified framework for solving both forward and inverse problems of differential equations, yet their performance and physical consistency strongly depend on how governing laws are incorporated. In this work, we present a systematic comparison of diffe…

• Deflation-PINNs: Learning Multiple Solutions for PDEs and Landau-de Gennes

  Sean Disar\`o, Ruma Rani Maity, Aras Bacho · 31 mars 2026

  Nonlinear Partial Differential Equations (PDEs) are ubiquitous in mathematical physics and engineering. Although Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving PDE problems, they typically struggle to identify multiple distinct solutions, since they are designed…

• Correcting Auto-Differentiation in Neural-ODE Training

  Yewei Xu, Shi Chen, Qin Li · 31 mars 2026

  Does the use of auto-differentiation yield reasonable updates for deep neural networks (DNNs)? Specifically, when DNNs are designed to adhere to neural ODE architectures, can we trust the gradients provided by auto-differentiation? Through mathematical analysis and numerical evidence, we demonstrate…

• Improving ideal MHD equilibrium accuracy with physics-informed neural networks

  Timo Thun, Andrea Merlo, Rory Conlin, Dario Panici, Daniel B\"ockenhoff · 31 mars 2026

  We present a novel approach to compute three-dimensional Magnetohydrodynamic equilibria by parametrizing Fourier modes with artificial neural networks and compare it to equilibria computed by conventional solvers. The full nonlinear global force residual across the volume in real space is then minim…

• DSO: Dual-Scale Neural Operators for Stable Long-term Fluid Dynamics Forecasting

  Huanshuo Dong, Hao Wu, Hong Wang, Qin-Yi Zhang, Zhezheng Hao · 31 mars 2026

  Long-term fluid dynamics forecasting is a critically important problem in science and engineering. While neural operators have emerged as a promising paradigm for modeling systems governed by partial differential equations (PDEs), they often struggle with long-term stability and precision. We identi…

• Automatic feature identification in least-squares policy iteration using the Koopman operator framework

  Christian Mugisho Zagabe, Sebastian Petiz · 30 mars 2026

  In this paper, we present a Koopman autoencoder-based least-squares policy iteration (KAE-LSPI) algorithm in reinforcement learning (RL). The KAE-LSPI algorithm is based on reformulating the so-called least-squares fixed-point approximation method in terms of extended dynamic mode decomposition (EDM…

• The internal law of a material can be discovered from its boundary

  Francesco Regazzoni · 30 mars 2026

  Since the earliest stages of human civilization, advances in technology have been tightly linked to our ability to understand and predict the mechanical behavior of materials. In recent years, this challenge has increasingly been framed within the broader paradigm of data-driven scientific discovery…

• Constitutive parameterized deep energy method for solid mechanics problems with random material parameters

  Zhangyong Liang, Huanhuan Gao · 30 mars 2026

  In practical structural design and solid mechanics simulations, material properties inherently exhibit random variations within bounded intervals. However, evaluating mechanical responses under continuous material uncertainty remains a persistent challenge. Traditional numerical approaches, such as …