{"url":"/method/neural-adjoint","slug":"neural-adjoint","name":"Neural adjoint","full_name":"Neural adjoint method","full_name_withheld":false,"description_markdown":"The NA method can be divided into two steps: (i) Training a neural network approximation of f , and (ii) inference of xˆ. Step (i) is conventional and involves training a generic neural network on a dataset\r\nˆ\r\nof input/output pairs from the simulator, denoted D, resulting in f, an approximation of the forward ˆ\r\nmodel. This is illustrated in the left inset of Fig 1. In step (ii), our goal is to use ∂f/∂x to help us gradually adjust x so that we achieve a desired output of the forward model, y. This is similar to many classical inverse modeling approaches, such as the popular Adjoint method [8, 9]. For many practical\r\nˆ\r\nexpression for the simulator, from which it is trivial to compute ∂f/∂x, and furthermore, we can use modern deep learning software packages to efficiently estimate gradients, given a loss function L.\r\nMore formally, let y be our target output, and let xˆi be our current estimate of the solution, where i indexes each solution we obtain in an iterative gradient-based estimation procedure. Then we compute xˆi+1 with\r\ninverse problems, however, obtaining ∂f/∂x requires significant expertise and/or effort, making these approaches challenging. Crucially, fˆ from step (i) provides us with a closed-form differentiable","description_state":"present","introduced_year":null,"introduced_by":{"title":"Benchmarking deep inverse models over time, and the neural-adjoint method","paper":"/paper/benchmarking-deep-inverse-models-over-time","first_author":"Simiao Ren","n_authors":3,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/benchmarking-deep-inverse-models-over-time"},"source":{"url":"https://arxiv.org/abs/2009.12919v4","title":"Benchmarking deep inverse models over time, and the neural-adjoint method","url_on_a_paper_host":true},"code_snippet_url":null,"code_snippet_url_on_a_code_host":false,"categories":[{"area":"General","area_id":"general","collection":"Optimization","url":"/methods/category/optimization","pwc_aliases":[]}],"n_papers_tagged":3,"archive_num_papers":3,"papers_newest_first":[{"paper":"/paper/enhancing-inverse-problem-solutions-with","title":"Enhancing Inverse Problem Solutions with Accurate Surrogate Simulators and Promising Candidates","date":"2023-04-26","arxiv_id":"2304.13860","n_code_links":1,"syntology":null},{"paper":"/paper/inverse-deep-learning-methods-and-benchmarks","title":"Inverse deep learning methods and benchmarks for artificial electromagnetic material design","date":"2021-12-19","arxiv_id":"2112.10254","n_code_links":2,"syntology":null},{"paper":"/paper/benchmarking-deep-inverse-models-over-time","title":"Benchmarking deep inverse models over time, and the neural-adjoint method","date":"2020-09-27","arxiv_id":"2009.12919","n_code_links":1,"syntology":{"ran":2,"of":2,"unverified":0,"pointer_only":2}}],"papers_shown":3,"tasks":[{"task":"/task/benchmarking","name":"Benchmarking","papers":1},{"task":"/task/robust-design","name":"Robust Design","papers":1}],"tasks_shown":2,"n_tasks":2,"usage_by_year":[{"year":"2020","papers":1},{"year":"2021","papers":1},{"year":"2023","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/neural-adjoint"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}