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• PIML and Kolmogorov-Arnold Networks (KANs)

Physics-Informed Machine Learning (PIML) and Kolmogorov-Arnold Networks (KANs)

Abstract

In this seminar talk at Caltech’s CMX, I present recent advancements in Physics-Informed Machine Learning (PIML) and our approach using Kolmogorov-Arnold Networks (KANs). The talk covers key concepts and practical case studies, including:

CMX: http://cmx.caltech.edu/

1️⃣ Introduction to PIML and Enhancements

2️⃣ Case Study: Inferring Hidden Turbulent Temperature Fields from Sparse Velocity Measurements

3️⃣ Kůrková Kolmogorov-Arnold Networks (KKANs): Introduction and Examples

4️⃣ Learning Dynamics in PIML via the Information Bottleneck Theory

Publications

During this talk, I discuss insights from several of our recent publications, including:

📄 “From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning” - https://arxiv.org/abs/2410.13228

📄 “Inferring Turbulent Velocity and Temperature Fields using Kolmogorov-Arnold Networks” - https://arxiv.org/abs/2407.15727

📄 “KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics” - https://arxiv.org/abs/2412.16738

📄 “Learning in PINNs: Phase Transition, Total Diffusion, and Generalization” - https://arxiv.org/abs/2403.18494

📄 “A Comprehensive and FAIR Comparison between MLP and KAN Representations” - https://arxiv.org/abs/2406.02917

📄 “Residual-Based Attention in Physics-Informed Neural Networks” - https://www.sciencedirect.com/science/article/abs/pii/S0045782524000616