Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs
A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Leveraging Hamilton-Jacobi PDEs with time-dependent Hamiltonians for continual scientific machine learning
We address two major challenges in scientific machine learning (SciML): interpretability and computational efficiency. We increase the interpretability of certain learning processes by establishing a new theoretical conn…
Computational EfficiencyContinual LearningFrom multi-dimensional black scholes to Hamilton jacobi
The first widely used financial model is linked to dynamical Hamilton jacobi model
VQEzy: An Open-Source Dataset for Parameter Initialization in Variational Quantum Eigensolvers
Variational Quantum Eigensolvers (VQEs) are a leading class of noisy intermediate-scale quantum (NISQ) algorithms, whose performance is highly sensitive to parameter initialization. Although recent machine learning-based…
Computation of Reachable Sets Based on Hamilton-Jacobi-Bellman Equation with Running Cost Function
A novel method for computing reachable sets is proposed in this paper. In the proposed method, a Hamilton-Jacobi-Bellman equation with running cost functionis numerically solved and the reachable sets of different time h…
On the Fragility of the Basis on the Hamilton-Jacobi-Bellman Equation in Economic Dynamics
In this paper, we provide an example of the optimal growth model in which there exist infinitely many solutions to the Hamilton-Jacobi-Bellman equation but the value function does not satisfy this equation. We consider t…