{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/approximating-the-solution-to-wave","title":"Approximating the solution to wave propagation using deep neural networks","arxiv_id":"1812.01609","date":"2018-12-04","proceeding":null,"authors":["Wilhelm E. Sorteberg","Stef Garasto","Alison S. Pouplin","Chris D. Cantwell","Anil A. Bharath"],"abstract":"Humans gain an implicit understanding of physical laws through observing and\ninteracting with the world. Endowing an autonomous agent with an understanding\nof physical laws through experience and observation is seldom practical: we\nshould seek alternatives. Fortunately, many of the laws of behaviour of the\nphysical world can be derived from prior knowledge of dynamical systems,\nexpressed through the use of partial differential equations. In this work, we\nsuggest a neural network capable of understanding a specific physical\nphenomenon: wave propagation in a two-dimensional medium. We define\n`understanding' in this context as the ability to predict the future evolution\nof the spatial patterns of rendered wave amplitude from a relatively small set\nof initial observations. The inherent complexity of the wave equations --\ntogether with the existence of reflections and interference -- makes the\nprediction problem non-trivial. A network capable of making approximate\npredictions also unlocks the opportunity to speed-up numerical simulations for\nwave propagation. To this aim, we created a novel dataset of simulated wave\nmotion and built a predictive deep neural network comprising of three main\nblocks: an encoder, a propagator made by 3 LSTMs, and a decoder. Results show\nreasonable predictions for as long as 80 time steps into the future on a\ndataset not seen during training. Furthermore, the network is able to\ngeneralize to an initial condition that is qualitatively different from those\nseen during training.","url_abs":"http://arxiv.org/abs/1812.01609v1","url_pdf":"http://arxiv.org/pdf/1812.01609v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"approximating-the-solution-to-wave","repo_url":"https://github.com/stathius/wave_propagation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}