Related papers: Adjoint-based gradient methods for inverse design …
Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…
In this work, we revisit a classical distributed gradient-descent algorithm, introducing an interesting class of perturbed multi-agent systems. The state of each subsystem represents a local estimate of a solution to the global optimization…
Generative models are powerful tools for sampling from a learned distribution $\mathcal{P}(Y \mid X)$, and inverse-design methods invert this map to find an input $x$ that produces a desired point output $y^*$. However, many design goals…
This paper interprets the stabilized finite element method via residual minimization as a variational multiscale method. We approximate the solution to the partial differential equations using two discrete spaces that we build on a…
Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…
Multidisciplinary engineering system design typically employs a sequential process, progressing from system dynamics to design variables and control. However, this process is inefficient and may lead to a suboptimal design. We propose…
We consider a general optimal control problem in the setting of gradient flows. Two approximations of the problem are presented, both relying on the variational reformulation of gradient-flow dynamics via the Weighted-Energy-Dissipation…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
Conductivity reconstruction in an inverse eddy current problem is considered in the present paper. With the electric field measurement on part of domain boundary, we formulate the reconstruction problem to a constrained optimization problem…
We present a method for computing A-optimal sensor placements for infinite-dimensional Bayesian linear inverse problems governed by PDEs with irreducible model uncertainties. Here, irreducible uncertainties refers to uncertainties in the…
Feedback optimization is an increasingly popular control paradigm to optimize dynamical systems, accounting for control objectives that concern the system operation at steady-state. Existing feedback optimization techniques heavily rely on…
In computational inverse problems, the optimal experimental design (OED) problem seeks the best locations in time and space at which to take measurements. We investigate the nonlinear OED problem in the context of continuously-indexed…
In this paper we consider the inverse problem of identifying the initial data in a fractionally damped wave equation from time trace measurements on a surface, as relevant in photoacoustic or thermoacoustic tomography. We derive and analyze…
Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…
Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
This paper is concerned with two-block separable convex minimization problems with linear constraints, for which it is either impossible or too expensive to obtain the exact solutions of the subproblems involved in the proximal ADMM…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
A new gradient-based adaptive sampling method is proposed for design of experiments applications which balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. High…