惯性聚合 高效追踪和阅读你感兴趣的博客、新闻、科技资讯
阅读原文 在惯性聚合中打开

推荐订阅源

V
V2EX
量子位
博客园 - 司徒正美
IT之家
IT之家
V
Visual Studio Blog
Apple Machine Learning Research
Apple Machine Learning Research
博客园_首页
Google DeepMind News
Google DeepMind News
Last Week in AI
Last Week in AI
Microsoft Security Blog
Microsoft Security Blog
T
Tailwind CSS Blog
aimingoo的专栏
aimingoo的专栏
GbyAI
GbyAI
Vercel News
Vercel News
B
Blog
大猫的无限游戏
大猫的无限游戏
D
DataBreaches.Net
小众软件
小众软件
罗磊的独立博客
博客园 - 叶小钗
雷峰网
雷峰网
Martin Fowler
Martin Fowler
Hugging Face - Blog
Hugging Face - Blog
WordPress大学
WordPress大学

stat.ML updates on arXiv.org

Adaptive multi-fidelity optimization with fast learning rates Enhancing AI and Dynamical Subseasonal Forecasts with Probabilistic Bias Correction Sample Complexity Bounds for Stochastic Shortest Path with a Generative Model The Harder Path: Last Iterate Convergence for Uncoupled Learning in Zero-Sum Games with Bandit Feedback Stylistic-STORM (ST-STORM) : Perceiving the Semantic Nature of Appearance Collective Kernel EFT for Pre-activation ResNets PRIM-cipal components analysis One-Shot Generative Flows: Existence and Obstructions Structural interpretability in SVMs with truncated orthogonal polynomial kernels Amortized Optimal Transport from Sliced Potentials MinShap: A Modified Shapley Value Approach for Feature Selection Unsupervised feature selection using Bayesian Tucker decomposition Multi-User mmWave Beam and Rate Adaptation via Combinatorial Satisficing Bandits Best of both worlds: Stochastic & adversarial best-arm identification Scalable Model-Based Clustering with Sequential Monte Carlo Expert-Guided Class-Conditional Goodness-of-Fit Scores for Interpretable Classification with Informative Missingness: An Application to Seismic Monitoring Lightweight Geometric Adaptation for Training Physics-Informed Neural Networks Gating Enables Curvature: A Geometric Expressivity Gap in Attention Zeroth-Order Optimization at the Edge of Stability Differentially Private Conformal Prediction CLion: Efficient Cautious Lion Optimizer with Enhanced Generalization Generative Augmented Inference Improving Machine Learning Performance with Synthetic Augmentation PAC-MCTS: Bias-Aware Pruning for Robust LLM-Guided Search and Planning Path-Sampled Integrated Gradients Heat and Matérn Kernels on Matchings Doubly Outlier-Robust Online Infinite Hidden Markov Model Momentum Further Constrains Sharpness at the Edge of Stochastic Stability Multistage Conditional Compositional Optimization BOAT: Navigating the Sea of In Silico Predictors for Antibody Design via Multi-Objective Bayesian Optimization
Improved Training of Physics-Informed Neural Networks wit...
Katsiaryna Haitsiukevich, Alexander Ilin · 2022-04-11 · via stat.ML updates on arXiv.org

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training such physics-informed neural networks (PINNs) is notoriously difficult in practice since PINNs often converge to wrong solutions. In this paper, we address this problem by training an ensemble of PINNs. Our approach is motivated by the observation that individual PINN models find similar solutions in the vicinity of points with targets (e.g., observed data or initial conditions) while their solutions may substantially differ farther away from such points. Therefore, we propose to use the ensemble agreement as the criterion for gradual expansion of the solution interval, that is including new points for computing the loss derived from differential equations. Due to the flexibility of the domain expansion, our algorithm can easily incorporate measurements in arbitrary locations. In contrast to the existing PINN algorithms with time-adaptive strategies, the proposed algorithm does not need a pre-defined schedule of interval expansion and it treats time and space equally. We experimentally show that the proposed algorithm can stabilize PINN training and yield performance competitive to the recent variants of PINNs trained with time adaptation.