Related papers: Merging automatic differentiation and the adjoint …

This paper considers the problem of distributed model fitting using the alternating directions method of multipliers (ADMM). ADMM splits the learning problem into several smaller subproblems, usually by partitioning the data samples. The…

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

The design of a stellarator with acceptable confinement properties requires optimization of the magnetic field in the non-convex, high-dimensional spaces describing their geometry. Another major challenge facing the stellarator program is…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We propose a general framework for differentiating shapes represented in binary images with respect to their parameters. This framework functions as an automatic differentiation tool for shape parameters, generating both binary density maps…

A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

Graded-index optical elements are capable of shaping light precisely and in very specific ways. While classical freeform optics uses only a two-dimensional domain such as the surface of a lens, recent technological advances in laser…

The differentiable programming paradigm is a cornerstone of modern scientific computing. It refers to numerical methods for computing the gradient of a numerical model's output. Many scientific models are based on differential equations,…

Nanophotonic device design aims to optimize photonic structures to meet specific requirements across various applications. Inverse design has unlocked non-intuitive, high-dimensional design spaces, enabling the discovery of high-performance…

One of the crucial issues in federated learning is how to develop efficient optimization algorithms. Most of the current ones require full device participation and/or impose strong assumptions for convergence. Different from the widely-used…

The adjoint sensitivity method scalably computes gradients of solutions to ordinary differential equations. We generalize this method to stochastic differential equations, allowing time-efficient and constant-memory computation of gradients…

Gradient-based algorithms are crucial to modern computer-vision and graphics applications, enabling learning-based optimization and inverse problems. For example, photorealistic differentiable rendering pipelines for color images have been…

The development of low-loss reconfigurable integrated optical devices enables further research into technologies including photonic signal processing, analogue quantum computing, and optical neural networks. Here, we introduce digital…

We present a proof-of-concept technique for the inverse design of electromagnetic devices motivated by the policy gradient method in reinforcement learning, named PHORCED (PHotonic Optimization using REINFORCE Criteria for Enhanced Design).…

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…

A novel and highly efficient computational framework for reconstructing binary-type images suitable for models of various complexity seen in diverse biomedical applications is developed and validated. Efficiency in computational speed and…

The inverse design approach in magnonics exploits the wave nature of magnons and machine learning to develop logical devices with functionalities that exceed the capabilities of analytical methods. While promising for analog, Boolean, and…

This paper proposes a new equation from continuous adjoint theory to compute the gradient of quantities governed by the Transport Theory of light. Unlike discrete gradients ala autograd, which work at the code level, we first formulate the…

Stencil loops are a common motif in computations including convolutional neural networks, structured-mesh solvers for partial differential equations, and image processing. Stencil loops are easy to parallelise, and their fast execution is…