Related papers: Multi-Trajectory Physics-Informed Neural Networks …

The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…

We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…

We treat infinite horizon optimal control problems by solving the associated stationary Hamilton-Jacobi-Bellman (HJB) equation numerically to compute the value function and an optimal feedback law. The dynamical systems under consideration…

We discuss nonlinear model predictive control (NMPC) for multi-body dynamics via physics-informed machine learning methods. Physics-informed neural networks (PINNs) are a promising tool to approximate (partial) differential equations. PINNs…

This paper addresses the problem of planning time-optimal trajectories for multiple cooperative agents along specified paths through a static road network. Vehicle interactions at intersections create non-trivial decisions, with complex…

We present HyPINO, a multi-physics neural operator designed for zero-shot generalization across a broad class of PDEs without requiring task-specific fine-tuning. Our approach combines a Swin Transformer-based hypernetwork with mixed…

We introduce a sampling based machine learning approach, Monte Carlo physics informed neural networks (MC-PINNs), for solving forward and inverse fractional partial differential equations (FPDEs). As a generalization of physics informed…

We propose a consistent physics-informed neural networks (CPINNs) framework for elliptic obstacle problems formulated as variational inequalities. The method is based on a mixed loss functional that is rigorously aligned with the stability…

We present a Physics-Informed Neural Network (PINN) framework for reconstructing the redshift-dependent Hubble parameter \(H(z)\) within the Tsallis Holographic Dark Energy (THDE) model extended by massive neutrinos. In this approach, the…

This paper presents a new methodology to craft navigation functions for nonlinear systems with stochastic uncertainty. The method relies on the transformation of the Hamilton-Jacobi-Bellman (HJB) equation into a linear partial differential…

We propose Weak and Entropy PINNs (WE-PINNs) for the approximation of entropy solutions to nonlinear hyperbolic conservation laws. Standard physics-informed neural networks enforce governing equations in strong differential form, an…

We propose a class of numerical schemes for nonlocal HJB variational inequalities (HJBVIs) with monotone drivers. The solution and free boundary of the HJBVI are constructed from a sequence of penalized equations, for which a continuous…

For an infinite-horizon control problem, the optimal control can be represented by the stable manifold of the characteristic Hamiltonian system of Hamilton-Jacobi-Bellman (HJB) equation in a semiglobal domain. In this paper, we first…

The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…

Physics-informed neural networks (PINNs) are a new tool for solving boundary value problems by defining loss functions of neural networks based on governing equations, boundary conditions, and initial conditions. Recent investigations have…

Steady-state electrothermal systems involve strongly coupled heat transfer, fluid flow, and electric-potential transport, creating severe numerical challenges for standard physics-informed neural networks (PINNs) due to stark disparities in…

This paper studies the finite horizon portfolio management by optimally tracking a ratcheting capital benchmark process. It is assumed that the fund manager can dynamically inject capital into the portfolio account such that the total…

In this paper, we propose a hybrid MPC local planner that uses a learning-based approximation of a time-varying safe set, derived from local observations and applied as the MPC terminal constraint. This set can be represented as a…

Compared with conventional numerical approaches to solving partial differential equations (PDEs), physics-informed neural networks (PINN) have manifested the capability to save development effort and computational cost, especially in…

We propose a reachability approach for infinite and finite horizon multi-objective optimization problems for low-thrust spacecraft trajectory design. The main advantage of the proposed method is that the Pareto front can be efficiently…