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Many machine learning models, such as logistic regression~(LR) and support vector machine~(SVM), can be formulated as composite optimization problems. Recently, many distributed stochastic optimization~(DSO) methods have been proposed to…
Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by timescale separation,…
Most inverse problems from physical sciences are formulated as PDE-constrained optimization problems. This involves identifying unknown parameters in equations by optimizing the model to generate PDE solutions that closely match measured…
Optimal control problems with nonsmooth objectives and nonlinear partial differential equation (PDE) constraints are challenging, mainly because of the underlying nonsmooth and nonconvex structures and the demanding computational cost for…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Optimization-based samplers such as randomize-then-optimize (RTO) [2] provide an efficient and parallellizable approach to solving large-scale Bayesian inverse problems. These methods solve randomly perturbed optimization problems to draw…
In this paper, we study the landscape of an online nonconvex optimization problem, for which the input data vary over time and the solution is a trajectory rather than a single point. To understand the complexity of finding a global…
This contribution presents an improved low-order 3D finite element formulation with hourglass stabilization using automatic differentiation (AD). Here, the former Q1STc formulation is enhanced by an approximation-free computation of the…
The spatially discretized magnetic vector potential formulation of magnetoquasistatic field problems is transformed from an infinitely stiff differential algebraic equation system into a finitely stiff ordinary differential equation (ODE)…
Matrix-variate optimization plays a central role in advanced wireless system designs. In this paper, we aim to explore optimal solutions of matrix variables under two special structure constraints using complex matrix derivatives, including…
The simulation and parameter optimization of coupled ocean circulation and ecosystem models in three space dimensions is one of the most challenging tasks in numerical climate research. Here we present a scientific toolkit that aims at…
A promising technique for the spectral design of acoustic metamaterials is based on the formulation of suitable constrained nonlinear optimization problems. Unfortunately, the straightforward application of classical gradient-based…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
We present a new method based on functional tensor decomposition and dynamic tensor approximation to compute the solution of a high-dimensional time-dependent nonlinear partial differential equation (PDE). The idea of dynamic approximation…
Many scientific and engineering challenges can be formulated as optimization problems which are constrained by partial differential equations (PDEs). These include inverse problems, control problems, and design problems. As a major…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
The efficient computation of Jacobians represents a fundamental challenge in computational science and engineering. Large-scale modular numerical simulation programs can be regarded as sequences of evaluations of in our case differentiable…
This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…