9 papers
Green-Routed Neural Operators: Physics Determines Where the Network Reads
Chenhao Si, Ming Yan
We identify a mismatch between the physical role of transport fields in many PDEs and their usual role in neural operators: PDEs use them to select read coordinates, whereas neural…
From Non-Convex Self-Concordant Regularization to Scalable Quasi-Newton Training of PINNs
Chenhao Si, Kang An, Shiqian Ma +1
Physics-informed neural networks (PINNs) often require high-accuracy quasi-Newton refinement to obtain reliable partial differential equation solutions, but their residual objectiv…
Newton Method for Fixed-Support Doubly Entropic Wasserstein Barycenter
Jianting Pan, Sirong Dai, Lei Yang +3
We study the fixed-support doubly regularized Wasserstein barycenter problem. Using the semi-dual formulation of entropic optimal transport, we reformulate the problem as a smooth,…
Inexact Bregman Sparse Newton Method for Efficient Optimal Transport
Jianting Pan, Ji'an Li, Ming Yan
Computing exact Optimal Transport (OT) distances for large-scale datasets is computationally prohibitive. While entropy-regularized alternatives offer speed, they sacrifice precisi…
AutoBalance: An Automatic Balancing Framework for Training Physics-Informed Neural Networks
Kang An, Chenhao Si, Ming Yan +1
Physics-Informed Neural Networks (PINNs) provide a powerful and general framework for solving Partial Differential Equations (PDEs) by embedding physical laws into loss functions.…
Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective
Chenhao Si, Ming Yan
Physics-informed neural networks (PINNs) are extensively employed to solve partial differential equations (PDEs) by ensuring that the outputs and gradients of deep learning models…
Complex Physics-Informed Neural Network
Chenhao Si, Ming Yan, Xin Li +1
We propose compleX-PINN, a novel physics-informed neural network (PINN) architecture incorporating a learnable activation function inspired by the Cauchy integral theorem. By optim…
Improving Discrete Optimisation Via Decoupled Straight-Through Estimator
Rushi Shah, Mingyuan Yan, Michael Curtis Mozer +1
The Straight-Through Estimator (STE) is the dominant method for training neural networks with discrete variables, enabling gradient-based optimisation by routing gradients through…
Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)
Chenhao Si, Ming Yan
We propose a new physics-informed neural network framework, IDPINN, based on the enhancement of initialization and domain decomposition to improve prediction accuracy. We train a P…