Model Reduction and Neural Networks

Derniers papiers

• Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

  Xander de Wit, Alessandro Gabbana, Michael Woodward, Yen Ting Lin, Federico Toschi, Daniel Livescu · 27 mars 2026

  The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the…

• A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems

  Tianlin Yang, Hailiang Du, Louis Aslett · 27 mars 2026

  Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting approaches, whether physics-based or neural-network-based, rema…

• Learning Mesh-Free Discrete Differential Operators with Self-Supervised Graph Neural Networks

  Lucas Gerken Starepravo, Georgios Fourtakas, Steven Lind, Ajay B. Harish, Tianning Tang, Jack R. C. King · 27 mars 2026

  Mesh-free numerical methods provide flexible discretisations for complex geometries; however, classical meshless discrete differential operators typically trade low computational cost for limited accuracy or high accuracy for substantial per-stencil computation. We introduce a parametrised framework…

• Spatiotemporal System Forecasting with Irregular Time Steps via Masked Autoencoder

  Kewei Zhu, Yanze Xin, Jinwei Hu, Xiaoyuan Cheng, Yiming Yang, Sibo Cheng · 27 mars 2026

  Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational techniques, reducing prediction accuracy. To address these limitati…

• System-Anchored Knee Estimation for Low-Cost Context Window Selection in PDE Forecasting

  Wenshuo Wang, Fan Zhang · 27 mars 2026

  Autoregressive neural PDE simulators predict the evolution of physical fields one step at a time from a finite history, but low-cost context-window selection for such simulators remains an unformalized problem. Existing approaches to context-window selection in time-series forecasting include exhaus…

• Improving Infinitely Deep Bayesian Neural Networks with Nesterov's Accelerated Gradient Method

  Chenxu Yu, Wenqi Fang · 27 mars 2026

  As a representative continuous-depth neural network approach, stochastic differential equation (SDE)-based Bayesian neural networks (BNNs) have attracted considerable attention due to their solid theoretical foundations and strong potential for real-world applications. However, their reliance on num…

• Stochastic Dimension-Free Zeroth-Order Estimator for High-Dimensional and High-Order PINNs

  Zhangyong Liang, Ji Zhang · 26 mars 2026

  Physics-Informed Neural Networks (PINNs) for high-dimensional and high-order partial differential equations (PDEs) are primarily constrained by the $\mathcal{O}(d^k)$ spatial derivative complexity and the $\mathcal{O}(P)$ memory overhead of backpropagation (BP). While randomized spatial estimators s…

• An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation

  Fangzhou Yu, Yiqi Su, Ray Lee, Shenfeng Cheng, Naren Ramakrishnan · 26 mars 2026

  Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn, this can compound error in long-horizon prediction and surr…

• Deep Neural Networks as Discrete Dynamical Systems: Implications for Physics-Informed Learning

  Abhisek Ganguly, Santosh Ansumali, Sauro Succi · 26 mars 2026

  We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between the numerical/exact solutions of the Burgers' and Eikonal eq…

• Resolving gradient pathology in physics-informed epidemiological models

  Nickson Golooba, Woldegebriel Assefa Woldegerima · 26 mars 2026

  Physics-informed neural networks (PINNs) are increasingly used in mathematical epidemiology to bridge the gap between noisy clinical data and compartmental models, such as the susceptible-exposed-infected-removed (SEIR) model. However, training these hybrid networks is often unstable due to competin…

• Project and Generate: Divergence-Free Neural Operators for Incompressible Flows

  Xigui Li, Hongwei Zhang, Ruoxi Jiang, Deshu Chen, Chensen Lin, Limei Han, Yuan Qi, Xin Guo, Yuan Cheng · 26 mars 2026

  Learning-based models for fluid dynamics often operate in unconstrained function spaces, leading to physically inadmissible, unstable simulations. While penalty-based methods offer soft regularization, they provide no structural guarantees, resulting in spurious divergence and long-term collapse. In…

• Latent Algorithmic Structure Precedes Grokking: A Mechanistic Study of ReLU MLPs on Modular Arithmetic

  Anand Swaroop · 26 mars 2026

  Grokking-the phenomenon where validation accuracy of neural networks on modular addition of two integers rises long after training data has been memorized-has been characterized in previous works as producing sinusoidal input weight distributions in transformers and multi-layer perceptrons (MLPs). W…

• Residual Attention Physics-Informed Neural Networks for Robust Multiphysics Simulation of Steady-State Electrothermal Energy Systems

  Yuqing Zhou, Ze Tao, Fujun Liu · 26 mars 2026

  Efficient thermal management and precise field prediction are critical for the design of advanced energy systems, including electrohydrodynamic transport, microfluidic energy harvesters, and electrically driven thermal regulators. However, the steady-state simulation of these electrothermal coupled …

• Linear-Nonlinear Fusion Neural Operator for Partial Differential Equations

  Heng Wu, Junjie Wang, Benzhuo Lu · 26 mars 2026

  Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial differential equations (PDEs) - an advantage that is difficul…

• Kirchhoff-Inspired Neural Networks for Evolving High-Order Perception

  Tongfei Chen, Jingying Yang, Linlin Yang, Jinhu L\"u, David Doermann, Chunyu Xie, Long He, Tian Wang, Juan Zhang, Guodong Guo, Baochang Zhang · 26 mars 2026

  Deep learning architectures are fundamentally inspired by neuroscience, particularly the structure of the brain's sensory pathways, and have achieved remarkable success in learning informative data representations. Although these architectures mimic the communication mechanisms of biological neurons…

• Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learning

  Salah A Faroughi, Farinaz Mostajeran, Amirhossein Arzani, Shirko Faroughi · 26 mars 2026

  Symbolic discovery of governing equations is a long-standing goal in scientific machine learning, yet a fundamental trade-off persists between interpretability and scalable learning. Classical symbolic regression methods yield explicit analytic expressions but rely on combinatorial search, whereas n…

• UniFluids: Unified Neural Operator Learning with Conditional Flow-matching

  Haosen Li, Qi Meng, Jiahao Li, Rui Zhang, Ruihua Song, Liang Ma, Zhi-Ming Ma · 25 mars 2026

  Partial differential equation (PDE) simulation holds extensive significance in scientific research. Currently, the integration of deep neural networks to learn solution operators of PDEs has introduced great potential. In this paper, we present UniFluids, a conditional flow-matching framework that h…

• Artificial intelligence for partial differential equations in computational mechanics: A review

  Yizheng Wang, Jinshuai Bai, Zhongya Lin, Qimin Wang, Cosmin Anitescu, Jia Sun, Mohammad Sadegh Eshaghi, Yuantong Gu, Xi-Qiao Feng, Xiaoying Zhuang, Timon Rabczuk, Yinghua Liu · 25 mars 2026

  In recent years, Artificial intelligence (AI) has become ubiquitous, empowering various fields, especially integrating artificial intelligence and traditional science (AI for Science: Artificial intelligence for science), which has attracted widespread attention. In AI for Science, using artificial …

• Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning (ME-EQL)

  Maria-Veronica Ciocanel, John T. Nardini, Kevin B. Flores, Erica M. Rutter, Suzanne S. Sindi, Alexandria Volkening · 25 mars 2026

  Agent-based modeling (ABM) is a powerful tool for understanding self-organizing biological systems, but it is computationally intensive and often not analytically tractable. Equation learning (EQL) methods can derive continuum models from ABM data, but they typically require extensive simulations fo…

• Learning dynamically inspired bases for Koopman and transfer operator approximation

  Gary Froyland, Kevin K\"uhl · 25 mars 2026

  Transfer and Koopman operator methods offer a framework for representing complex, nonlinear dynamical systems via linear transformations, enabling a deeper understanding of the underlying dynamics. The spectra of these operators provide important insights into system predictability and emergent beha…

• Generalization Bounds for Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations

  Sebastien Andre-Sloan, Dibyakanti Kumar, Alejandro F Frangi, Anirbit Mukherjee · 25 mars 2026

  This work establishes rigorous first-of-its-kind upper bounds on the generalization error for the method of approximating solutions to the (d+1)-dimensional incompressible Navier-Stokes equations by training depth-2 neural networks trained via the unsupervised Physics-Informed Neural Network (PINN) …

• Weak-PDE-Net: Discovering Open-Form PDEs via Differentiable Symbolic Networks and Weak Formulation

  Xinxin Li, Xingyu Cui, Jin Qi, Juan Zhang, Da Li, Junping Yin · 25 mars 2026

  Discovering governing Partial Differential Equations (PDEs) from sparse and noisy data is a challenging issue in data-driven scientific computing. Conventional sparse regression methods often suffer from two major limitations: (i) the instability of numerical differentiation under sparse and noisy d…

• Problems with Chinchilla Approach 2: Systematic Biases in IsoFLOP Parabola Fits

  Eric Czech, Zhiwei Xu, Yael Elmatad, Yixin Wang, William Held · 25 mars 2026

  Chinchilla Approach 2 is among the most widely used methods for fitting neural scaling laws. Its parabolic approximation introduces systematic biases in compute-optimal allocation estimates, even on noise-free synthetic data. Applied to published Llama 3 IsoFLOP data at open frontier compute scales,…

• A graph neural network based chemical mechanism reduction method for combustion applications

  Manuru Nithin Padiyar, Priyabrat Dash, Konduri Aditya · 25 mars 2026

  Direct numerical simulations of turbulent reacting flows involving millions of grid points and detailed chemical mechanisms with hundreds of species and thousands of reactions are computationally prohibitive. To address this challenge, we present two data-driven chemical mechanism reduction formulat…

• Coordinate Encoding on Linear Grids for Physics-Informed Neural Networks

  Tetsuro Tsuchino, Motoki Shiga · 25 mars 2026

  In solving partial differential equations (PDEs), machine learning utilizing physical laws has received considerable attention owing to advantages such as mesh-free solutions, unsupervised learning, and feasibility for solving high-dimensional problems. An effective approach is based on physics-info…