相关论文: Adjoint-based gradient estimation from gray-box so…

In this study, we find the optimal control boundary (i.e., actuator velocity) that cancels the acoustic reverberations inside drop-on-demand inkjet printheads at a specific time. We formulate an optimization problem to minimize the total…

The method of characteristics is a classical method for gaining understanding in the solution of a partial differential equation. It has recently been applied to the adjoint equations of the 2D Euler equations and the first goal of this…

Many large-scale and distributed optimization problems can be brought into a composite form in which the objective function is given by the sum of a smooth term and a nonsmooth regularizer. Such problems can be solved via a proximal…

We explain how to compute gradients of functions of the form $G = \frac{1}{2} \sum_{i=1}^{m} (E y_i - C_i)^2$, which often appear in the calibration of stochastic models, using Automatic Adjoint Differentiation and parallelization. We…

In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…

Gradient-flow (GF) viewpoints unify and illuminate optimization algorithms, yet most GF analyses focus on unconstrained settings. We develop a geometry-respecting framework for constrained problems by (i) reparameterizing feasible sets with…

In this paper we propose a novel gradient algorithm to learn a policy from an expert's observed behavior assuming that the expert behaves optimally with respect to some unknown reward function of a Markovian Decision Problem. The…

A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear…

Isogeometric analysis was applied very successfully to many problem classes like linear elasticity, heat transfer and incompressible flow problems but its application to compressible flows is very rare. However, its ability to accurately…

Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…

Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal…

We investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…

Model Agnostic Meta Learning (MAML) is widely used to find a good initialization for a family of tasks. Despite its success, a critical challenge in MAML is to calculate the gradient w.r.t. the initialization of a long training trajectory…

There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC…

Gradient sampling (GS) has proved to be an effective methodology for the minimization of objective functions that may be nonconvex and/or nonsmooth. The most computationally expensive component of a contemporary GS method is the need to…

The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…

The direct method of construction of local conservation laws of partial differential equations (PDE) is a systematic method applicable to a wide class of PDE systems [Anco S. and Bluman G., Direct construction method for conservation laws…

With the success that the field of bilevel optimization has seen in recent years, similar methodologies have started being applied to solving more difficult applications that arise in trilevel optimization. At the helm of these applications…

The analytic properties of adjoint solutions are investigated for the two-dimensional (2D) full potential equation. For subcritical flows, the Green's function approach is used to derive the analytic adjoint solution for a cost function…

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…