Model Reduction and Neural Networks

Últimos artículos

• Learning Physics-Informed Surrogate Model of Linear Elastic Displacement Fields from Geometry

  Rodolphe Barlogis, Ferhat Tamssaouet, Quentin Falcoz, St\'ephane Grieu · 13 de julio de 2026

  This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains. We propose a physics-informed DeepONet framework that predicts displacement fields from both boundary conditions and fracture geometry, using a dedicate…

• Unlocking Temporal Generalization in Hamiltonian Video Dynamics Models

  Eli Laird, Corey Clark · 10 de julio de 2026

  World models are typically trained to predict discrete-time physical dynamics with a fixed step size baked into the model weights, preventing prediction at variable temporal resolutions. This matters for hierarchical planning, sim-to-real transfer, and scientific or game-engine applications that mus…

• LLT: Local Linear Transformer for PDE Operator Learning

  Oded Ovadia, Eli Turkel · 10 de julio de 2026

  Neural operators have become a common approach for learning PDE solution maps and accelerating numerical simulations. Transformer-based neural operators are of particular interest, since attention can learn long-range dependencies in the computational domain. However, standard attention has two majo…

• Neural non-canonical Hamiltonian dynamics for long-time simulations

  Cl\'ementine Court\`es (IRMA, MACARON), Emmanuel Franck (MACARON), Michael Kraus (IPP), Laurent Navoret (IRMA, MACARON), L\'eopold Tr\'emant (LML) · 10 de julio de 2026

  This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet, respectively with a potential-based architecture and with degen…

• Quantum simulation of real-world nonlinear dynamics via Koopman method

  Baoyang Zhang, Dong An, Zhaoyuan Meng, Yefei Yu, Xiaoxiao Xiao, Zhen Lu, Yue Yang · 9 de julio de 2026

  Nonlinear dynamics is ubiquitous in nature, ranging from chemical pattern formation to ocean circulation, yet its simulation on quantum computers is fundamentally limited by the unitary nature of quantum evolution. We propose the quantum Koopman method, a data-driven framework that embeds nonlinear …

• An optimal control approach for neural network architecture adaptation with a posteriori error estimation

  C G Krishnanunni, Thomas Scott, Tan Bui-Thanh · 9 de julio de 2026

  This work presents a novel approach for adapting neural network architecture along the depth based on a posteriori error estimation. By formulating neural network training as a continuous-time optimal control problem, we derive rigorous error estimates that quantify how approximation error distribut…

• Reliable mechanistic operator recovery with biologically-informed neural networks: principles for architecture and optimisation design

  Rebecca M. Crossley, Yuan Yin, Sarah L. Waters, Ruth E. Baker · 9 de julio de 2026

  Many biological processes are governed by complex dynamical mechanisms that remain incompletely understood despite increasing volumes of experimental data. Biologically-informed neural networks (BINNs) seek to address this challenge by embedding mechanistic differential equations into neural network…

• CaLiSym: Learning Symplectic Dynamics of Real-World Systems through Structured Canonical Lifts

  Aristotelis Papatheodorou, Pranav Vaidhyanathan, Natalia Ares, Ioannis Havoutis, Gerard J. Milburn · 9 de julio de 2026

  Physics-informed learning promises data-efficient and stable dynamics prediction, yet its strongest geometric guarantees have largely remained confined to closed conservative systems. This excludes many robotic systems of practical interest, where actuation, dissipation, and constraints continuously…

• Higher-Order Geometric Updates for Levenberg-Marquardt Method via Riemann Normal Coordinates

  Jianing Liu, Dong H. Zhang · 9 de julio de 2026

  Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects…

• A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems

  Sonal Ankush Chibire, Jenn-Terng Gau, Bo Zhang · 8 de julio de 2026

  Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process. This study presents a PINN-based framework for modeling transient elastodynamic wave propagation in bimat…

• Physics-Informed Neural Embeddings of PDE Solution Families

  Raul Jimenez, Svitlana Mayboroda, Pavlos Protopapas, Leonid Sarieddine, David N. Spergel, Pedro Taranc\'on-\'Alvarez · 8 de julio de 2026

  We introduce a physics-informed framework for learning finite-dimensional embeddings of solution families of partial differential equations. The method uses a multihead Physics-Informed Neural Network in which a shared body learns a latent manifold representing the solution space, while linear heads…

• In-span learning: adapting reduced-order models using their own predictions

  Amirpasha Hedayat, Laura Balzano, Karthik Duraisamy · 7 de julio de 2026

  Reduced-order models compress high-dimensional dynamics into low-dimensional representations that can be evaluated rapidly, but they lose accuracy when online dynamics drift beyond the training data. Adaptive methods address this by updating the subspace online with external, out-of-span information…

• Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability

  Ronald Katende · 7 de julio de 2026

  We study operator relevance in data-driven partial differential equation (PDE) discovery. Sparse residual methods can select terms that improve residual fit, but residual contribution is not the same as functional necessity. We formalize this distinction through counterfactual operator interventions…

• CSympNet-ID: conformal-symplectic map learning for linearly damped Hamiltonian systems

  Jiale Gong (School of Mathematics), Pengzhan Jin (National Engineering Laboratory for Big Data Analysis and Applications, Peking University, Beijing, China), Dongyang Kuang (School of Mathematics), Lu Li (School of Mathematics), Yifa Tang (State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China) · 7 de julio de 2026

  Learning dissipative dynamics from discrete observations is essential for reliable long-horizon prediction and physically meaningful parameter identification. For linearly damped Hamiltonian systems, the exact flow is generally not symplectic but conformally symplectic, contracting the canonical sym…

• Generative Inverse Design with Abstention via Diagonal Flow Matching

  Miguel de Campos, Werner Krebs, Hanno Gottschalk · 7 de julio de 2026

  Inverse design aims to find design parameters $x$ achieving target performance $y^*$. Generative approaches learn bidirectional mappings between designs and labels, enabling diverse solution sampling. However, standard conditional flow matching (CFM), when adapted to inverse problems by pairing labe…

• LiNO: Lifting based multiresolution neural operator

  Himanshu Pandey, Subham Patel, Ratikanta Behera · 7 de julio de 2026

  Recently, neural operators have shown promising outcomes for learning solution operators of differential equations directly from data. This framework learns a functional mapping from the parameter field to the solution field, enabling the prediction of an entire class of solutions rather than a spec…

• Reduced-Order Models: The Mother of World Models

  Rajat Ghosh · 7 de julio de 2026

  World models -- compressed latent representations of an environment that support action-conditioned prediction and planning -- are typically presented as a product of modern self-supervised learning. This paper argues that the functional anatomy of a world model was independently developed, deployed…

• Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation

  Bangti Jin, Longjun Wu · 7 de julio de 2026

  Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore, the convergence guarantee of stochastic gradient descent is…

• Advances in Neural Controlled Differential Equations

  Benjamin Walker · 7 de julio de 2026

  Many real-world systems evolve continuously, yet most machine learning models interpret time series as discrete sequences. Continuous-time approaches instead treat time series as samples from an underlying input path, a formulation that naturally accommodates irregularly sampled or oversampled data.…

• Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

  Markus Heinonen, Yair Shenfeld, Ricardo Baptista, Daniel Waxman, Dmitry Batenkov, Tim Cooijmans, Eli Bingham · 7 de julio de 2026

  Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant al…

• LRX-PINN: A Layer-Resolving XNet Physics-Informed Neural Network with Integrated Cauchy Activations for Convection-Dominated Problems

  Zihao Guo, Xin Li, Zhihong Xia · 7 de julio de 2026

  Convection-dominated convection-diffusion problems often develop thin layers, where the solution has sharp transition profiles and its derivatives are highly localized. This creates a structural mismatch for standard physics-informed neural networks (PINNs), whose trial spaces are not designed to ma…

• Target-Guided Selective Reweighting for Physics-Informed Neural Network Inverse Problems: A Transfer Learning Approach

  Qian Hu, Bin Fan, Yao Xiao, Zhicheng Lin, Meixin Xiong · 7 de julio de 2026

  Physics-informed neural networks (PINNs) encounter ill-posed optimization, loss competition, and parameter compensation in partial differential equation (PDE) inverse problems. Transfer learning can reuse representations from source tasks, but direct fine-tuning may introduce negative transfer when …

• Conditional Clifford-Steerable CNNs for PDE Modeling

  B\'alint L\'aszl\'o Szarvas, Maksim Zhdanov · 7 de julio de 2026

  We introduce Conditional Clifford-Steerable CNNs (C-CSCNNs), a unified framework that incorporates equivariance to arbitrary pseudo-Euclidean groups and significantly improves the expressivity of standard CSCNNs. We show that the kernel basis of the standard formulation is incomplete, limiting model…

• PDEFlow: Autonomous Agentic PDE Pipelines for Neural Operator Learning and Solver-Free Inference

  Akshat Jani, Prathamesh Gadekar, Sakhinana Sagar Srinivas, Venkataramana Runkana · 7 de julio de 2026

  We present PDEFlow, an autonomous agentic framework that turns user-level ODE and PDE descriptions into solver-backed neural-operator pipelines. The workflow links problem specification, data generation, operator training, and checkpoint-based inference. A stateful input graph converts multi-turn na…

• Quadrature-Aware Complex-Linear Neural Operator for Boundary-to-Field Prediction in Resonant Acoustics

  Muhammad Idrees Khan, Hua-Dong Yao · 7 de julio de 2026

  Repeated prediction of acoustic fields from spatially distributed boundary excitation is computationally expensive when each source realization requires a new wave simulation. This work introduces a quadrature-aware complex-linear boundary operator (CLBO) that maps complex normal velocity on a vibra…