Model Reduction and Neural Networks

Latest papers

• Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series

  S. V. Manivelan, Andrei Velichko, I. Manimehan · 8 June 2026

  Detecting transient chaos from scalar observations without governing equations represents a fundamental challenge in nonlinear dynamics. We propose a geometry-guided machine learning framework that unifies predictive trajectory divergence with macroscopic attractor morphology to track abrupt regime …

• Architecture Shapes Transfer Specificity in Implicit Neural Representations

  D Yang Eng · 8 June 2026

  Transfer in coordinate networks is often measured by warm-start gain, but whether that gain reflects source-specific structure or generic weight reuse is less clear. We study this question across three implicit neural representation (INR) families, SIREN, ReLU MLPs, and Fourier-feature MLPs, using c…

• Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming

  Shah Pallav Dhanendrakumar, Saikat Pal, Sitikantha Roy · 5 June 2026

  Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are of…

• Finite Element-Based Material Learning via Automatic Differentiation: Learning constitutive neural network models from full-field deformation data

  Matthias Knipper, Chenyi Ji, Malte Brand, Kevin Linka · 5 June 2026

  The identification of constitutive neural network models from heterogeneous full-field deformation data provides a robust alternative to traditional calibration methods based on homogeneous stress-strain experiments, particularly given the high dimensionality of trainable parameters. Existing approa…

• From Ticks to Flows: Dynamics of Neural Reinforcement Learning in Continuous Environments

  Saket Tiwari, Tejas Kotwal, George Konidaris · 4 June 2026

  We present a novel theoretical framework for deep reinforcement learning (RL) in continuous environments by modeling the problem as a continuous-time stochastic process, drawing on insights from stochastic control. Building on previous work, we introduce a viable model of actor-critic algorithm that…

• PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems

  Ismail Hassaballa, Mircea Lazar · 4 June 2026

  Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, a…

• Curvature-aware dynamic precision approach for physics-informed neural networks

  Yingjie Shao, Ioannis N. Athanasiadis, George van Voorn, Taniya Kapoor · 4 June 2026

  Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, recent studies show that PINN optimisation is sensitive to numerical precision. Existing implemen…

• Nonlocal Mean Field Schr\"{o}dinger Bridge with Learned Interactions

  Daisuke Inoue, Mathieu Lauri\`ere, Dante Kalise · 4 June 2026

  The Schr\"odinger Bridge Problem constructs a stochastic process that connects an initial distribution to a terminal distribution with minimum energy. This work considers its mean-field extension, the Mean-Field Schr\"odinger Bridge, for interacting particle systems. With nonlocal interactions, eval…

• Learning symplectic model reduction based on a approximation theorem of symplectic embeddings

  Liyi Feng, Yifa Tang, Yulin Xie, Ruili Zhang, Aiqing Zhu · 4 June 2026

  High-dimensional Hamiltonian systems play a central role in many scientific and engineering disciplines, with dynamics evolving on symplectic manifolds. Although deep learning provides powerful tools for constructing low-dimensional surrogates from data, the intrinsic symplectic structure is easily …

• Bagged Polynomial Regression and Neural Networks

  Sylvia Klosin, Jaume Vives-i-Bastida · 4 June 2026

  Climate and environmental applications increasingly rely on high-dimensional prediction from remote sensing and other scientific data. Neural networks (NN) can deliver strong accuracy in these settings, but they are often hard to audit and hard to align with domain knowledge. As an alternative, we p…

• Learning Control-Affine Reduced-Order Models via Autoencoders

  Ali Mjalled, Martin M\"onnigmann · 4 June 2026

  We present in this paper a framework for the identification of control-affine reduced-order models (ROMs). The proposed method utilizes autoencoders (AEs) to transform the high-dimensional states, and potentially the high-dimensional inputs, into reduced latent ones suitable for control-affine state…

• Deep Embedded Multiplicative DMD for Algebra-Preserving Koopman Learning

  Kelan Gray, Finlay Brown, Nicolas Boull\'e, Matthew J. Colbrook · 4 June 2026

  Koopman theory turns nonlinear dynamics into a linear spectral problem. In computation, however, everything depends on a hard finite-dimensional choice: the observables must be expressive, nearly invariant under the dynamics, and, ideally, compatible with composition. Deep Koopman methods learn flex…

• Certified Neural Approximations of Nonlinear Dynamics

  Frederik Baymler Mathiesen, Nikolaus Vertovec, Francesco Fabiano, Luca Laurenti, Alessandro Abate · 4 June 2026

  Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closene…

• Loss-Conditional PINNs for Parametric PDE Families

  Anna Lazareva, Alexander Tarakanov · 4 June 2026

  Physics-informed neural networks (PINNs) approximate solutions of ODEs and PDEs by minimising a weighted combination of residual, boundary, initial, and data losses. Their performance is often dominated by the choice of loss weights: a poor weighting can drive training to a degenerate solution in wh…

• A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model

  Jinchao Feng, Sui Tang · 3 June 2026

  In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution equations, where the interaction kernel defines a normalized, stat…

• Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

  Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu · 3 June 2026

  Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but learned PDE solvers have not undergone a comparable shift. Existi…

• A Quantitative Approximation Framework for Flow Distillation in Diffusion Models

  Weiguo Gao, Ming Li, Lei Shi, Hanfei Zhou · 3 June 2026

  We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps. Focusing on trajectory distillation for the probability-flow ODE, we show that local approximation errors can be strongly amplified in…

• Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

  Keke Wu, Yixuan Zhang, Jingrun Chen · 3 June 2026

  Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs). Existing architectures typically obtain expressivity by parameterizing integral kernels in prescribed transform dom…

• EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

  Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park · 3 June 2026

  Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, maki…

• Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

  Abhishek Chandra, Taniya Kapoor · 3 June 2026

  Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering. Physics-informed neural networks (PINNs) learn PDE solutions from governing equations. However, accurately capturing temporal evolution remains challenging. Recent sequence-…

• Samudra 2: Scaling Ocean Emulators across Resolutions

  Yuan Yuan, Jesse Rusak, Alexander Merose, Adam Subel, Pavel Perezhogin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna · 3 June 2026

  Ocean general circulation models (OGCMs) are essential to climate science but computationally expensive, limiting ensemble size and forcing scenarios. Neural emulators promise orders-of-magnitude speedups, yet existing ocean emulators have not combined fine spatial resolution with multi-year autoreg…

• Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

  Niccol\`o Perrone, Fanny Lehmann, Stefania Fresca, Filippo Gatti · 3 June 2026

  Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often …

• APIC: Amortized Physics-Informed Calibration using Neural Processes

  Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler · 3 June 2026

  Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, …

• Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction

  Ruiyuan Li, Ajay Seth, Manon Kok · 2 June 2026

  State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially …

• Learning Chaotic Dynamics through Second-Order Geometric Supervision

  Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh · 2 June 2026

  Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector fi…