Inverse Problems for Partial Differential Equations with Jump Discontinuities in Coefficients via Two-Stage Physics-Informed Deep Learning and Statistical Mixture Models

arXiv:2510.14656 · stat.ML, cs.LG · Submitted 2025-10-16 · Read on arXiv

stat.ML, cs.LG

Submitted: 2025-10-16

Updated: 2026-08-18

Code: https://github.com/Zhikun0416/Inverse-Problem

Terminology

• Inverse Problem — 44× in this paper · explained in 2 episodes
• Accuracy — 18× in this paper · explained in 1 episode
• Adaptive Weighting — 14× in this paper · explained in 1 episode
• Adam — 11× in this paper · explained in 2 episodes
• Clustering — 11× in this paper · explained in 2 episodes
• Robustness — 10× in this paper · explained in 5 episodes
• Ablation — 8× in this paper · explained in 1 episode
• Uncertainty Quantification — 8× in this paper · explained in 8 episodes
• Regularization — 7× in this paper · explained in 3 episodes
• Consistency — 6× in this paper · explained in 3 episodes
• Ablation study — 4× in this paper · explained in 1 episode
• Adaptability — 4× in this paper · explained in 1 episode
• Initial Data — 4× in this paper · explained in 2 episodes
• PDE residual — 4× in this paper · explained in 2 episodes
• Two-Stage Framework — 4× in this paper · explained in 2 episodes
• Markov Chain Monte Carlo — 3× in this paper
• Monte Carlo dropout — 3× in this paper · explained in 2 episodes
• Transfer Learning — 3× in this paper · explained in 10 episodes
• Activation Function — 2× in this paper · explained in 1 episode
• Adaptive Sampling — 2× in this paper · explained in 1 episode
• Bayesian Inference — 2× in this paper · explained in 5 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Interpretability — 2× in this paper · explained in 15 episodes
• Loss Function — 2× in this paper · explained in 2 episodes
• Computational Tractability — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Core — 1× in this paper · explained in 2 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Gaussian Mixture Model (GMM) — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Generative Adversarial Networks (GANs) — 1× in this paper · explained in 3 episodes
• Gradient Flow — 1× in this paper · explained in 2 episodes
• Latent Space — 1× in this paper · explained in 7 episodes
• Physical Constraints — 1× in this paper · explained in 7 episodes
• Physics-Informed Neural Networks (PINNs) — 1× in this paper · explained in 6 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Two-stage training — 1× in this paper · explained in 2 episodes

Related papers

• Behavior of prediction performance metrics with rare events
• Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
• A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
• Scalable Posterior Uncertainty for Flexible Density-Based Clustering
• A Transport Geometry of Benign Overfitting
• Efficient quadratic entropy with distance sketches