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Mathematical Foundations of AI for Control, Decision-Making, and Scientific Systems
Mathematical Foundations of AI for Control, Decision-Making, and Scientific Systems
Our research lies at the intersection of applied mathematics, optimal control, and machine learning.
I focus on Hamilton–Jacobi–Bellman (HJB) and Hamilton–Jacobi–Isaacs (HJI) equations that arise in stochastic optimal control, differential games, and risk-sensitive decision-making.
By combining rigorous PDE theory with physics-informed neural networks (PINNs), I develop neural policy iteration frameworks that overcome the curse of dimensionality while retaining theoretical guarantees.
AI driven mechanism design. The image is from the paper Deep reinforcement learning for optimal design of compliant mechanisms based on digitized cell structures published at Engineering Applications of AI.
Keywords: Hamilton–Jacobi Equations / Optimal Control / Differential Games / Physics-Informed Neural Networks / Scientific Machine Learning /Stochastic Control · Risk-Sensitive Decision-Making
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