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The Physics-Informed Neural Network (PINN) framework introduced recently incorporates physics into deep learning, and offers a promising avenue for the solution of partial differential equations (PDEs) as well as identification of the…

Differentiable optimization has attracted significant research interest, particularly for quadratic programming (QP). Existing approaches for differentiating the solution of a QP with respect to its defining parameters often rely on…

Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

In this paper, we focus on solving a class of constrained non-convex non-concave saddle point problems in a decentralized manner by a group of nodes in a network. Specifically, we assume that each node has access to a summand of a global…

Most of the existing recognition algorithms are proposed for closed set scenarios, where all categories are known beforehand. However, in practice, recognition is essentially an open set problem. There are categories we know called…

The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…

Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems.…

Mixed-integer quadratic programs (MIQPs) are a versatile way of formulating vehicle decision making and motion planning problems, where the prediction model is a hybrid dynamical system that involves both discrete and continuous decision…

In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…

Optical neural networks (ONNs), implemented on an array of cascaded Mach-Zehnder interferometers (MZIs), have recently been proposed as a possible replacement for conventional deep learning hardware. They potentially offer higher energy…

Plug-and-Play (PnP) is a non-convex optimization framework that combines proximal algorithms, for example, the alternating direction method of multipliers (ADMM), with advanced denoising priors. Over the past few years, great empirical…

In recent years, numerous vision and learning tasks have been (re)formulated as nonconvex and nonsmooth programmings(NNPs). Although some algorithms have been proposed for particular problems, designing fast and flexible optimization…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…

Physics-Informed Neural Networks (PINNs) are a novel computational approach for solving partial differential equations (PDEs) with noisy and sparse initial and boundary data. Although, efficient quantification of epistemic and aleatoric…

In the usual framework of control, a reference trajectory is needed as the set point for a feedback controller. This reference trajectory can be generated by solving a trajectory optimization problem. This problem is a continuous optimal…

We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…

This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…

Distributed, large-scale quantum computing will need architectures that combine matter-based qubits with photonic links, but today's software stacks target either gate-based chips or linear-optical devices in isolation. We introduce Optyx,…