1 citations · 2 across the 14 of their papers we have counts for
15 papers
Structure-Preserving Spectral Dynamic Programming on Compact Lie Groups
Shanqing Liu, Yang Qi
We study spectral approximations of the dynamic programming semigroup for finite-horizon optimal control on a connected compact Lie group , and of the associated first-order Ham…
Singularities in Multi-Objective Optimization and their Crossing during Continuation
Arjun Manoj, Michail E. Kavousanakis, Shanqing Liu +1
Continuation methods help trace Pareto sets in multi-objective optimization but are inherently local: a single run traces a single connected branch, requiring multiple restarts to…
PI-SONet: A Physics-Informed Symplectic Operator Network for Real-Time Optimal Control of Multi-Agent Systems
Alan John Varghese, Shanqing Liu, Paula Chen +3
Many real-life applications involve controlling high-dimensional multi-agent systems in real-time. Existing optimal control solvers often suffer from the curse-of-dimensionality an…
Tropical low-rank approximation and application to optimal control of N-body systems
Marianne Akian, Stephane Gaubert, Shanqing Liu +1
We study the approximation of the value function of deterministic optimal control problems with fixed initial state, motivated by \(N\)-body systems. In this setting, the action fu…
PINNs in PDE Constrained Optimal Control Problems: Direct vs Indirect Methods
Zhen Zhang, Shanqing Liu, Alessandro Alla +2
We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and…
Algorithms and Differential Game Representations for Exploring Nonconvex Pareto Fronts in High Dimensions
Shanqing Liu, Paula Chen, Youngkyu Lee +1
We develop a new Hamiton-Jacobi (HJ) and differential game approach for exploring the Pareto front of (constrained) multi-objective optimization (MOO) problems. Given a preference…
Adversarial Physics-Informed Machine Learning for Robust Optimal Safe Predefined-Time Stabilization: A Game-Theoretic Approach
Nick-Marios T. Kokolakis, Shanqing Liu, Jerome Darbon +2
We develop a game-theoretic framework for adversarially robust optimal safe predefined-time stabilization of parameter-dependent nonlinear dynamical systems with nonquadratic cost…
A Neural-Operator Preconditioned Newton Method for Accelerated Nonlinear Solvers
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We propose a novel neural preconditioned Newton (NP-Newton) method for solving parametric nonlinear systems of equations. To overcome the stagnation or instability of Newton iterat…
Automatic discovery of optimal meta-solvers for time-dependent nonlinear PDEs
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We present a general and scalable framework for the automated discovery of optimal meta-solvers for the solution of time-dependent nonlinear partial differential equations after ap…
Automatic selection of the best neural architecture for time series forecasting
Qianying Cao, Shanqing Liu, Alan John Varghese +3
Time series forecasting plays a pivotal role in a wide range of applications, including weather prediction, healthcare, structural health monitoring, predictive maintenance, energy…
Safe and Efficient Online Convex Optimization with Linear Budget Constraints and Partial Feedback
Shanqi Liu, Xin Liu
This paper studies online convex optimization with unknown linear budget constraints, where only the gradient information of the objective and the bandit feedback of constraint fun…
Automatic discovery of optimal meta-solvers via multi-objective optimization
Youngkyu Lee, Shanqing Liu, Jerome Darbon +1
We design two classes of ultra-fast meta-solvers for linear systems arising after discretizing PDEs by combining neural operators with either simple iterative solvers, e.g., Jacobi…
A time-dependent symplectic network for non-convex path planning problems with linear and nonlinear dynamics
Zhen Zhang, Chenye Wang, Shanqing Liu +2
We propose a novel neural network architecture (TSympOCNet) to address high--dimensional optimal control problems with linear and nonlinear dynamics. An important application of th…
Convergence and Error Estimates of A Semi-Lagrangian scheme for the Minimum Time Problem
Marianne Akian, Shanqing Liu
We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic…
Fast meta-solvers for 3D complex-shape scatterers using neural operators trained on a non-scattering problem
Youngkyu Lee, Shanqing Liu, Zongren Zou +5
Three-dimensional target identification using scattering techniques requires high accuracy solutions and very fast computations for real-time predictions in some critical applicati…