{"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/non-linear-independent-dual-system-nids-for","title":"Discretization-independent surrogate modeling over complex geometries using hypernetworks and implicit representations","arxiv_id":"2109.07018","date":"2021-09-14","proceeding":null,"authors":["James Duvall","Karthik Duraisamy","Shaowu Pan"],"abstract":"Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to decrease the computational expense while retaining dominant solution features and behavior. Traditional Convolutional Neural Network-based frameworks for surrogate modeling require lossy pixelization and data-preprocessing, and generally are not effective in realistic engineering applications. We propose alternative deep-learning based surrogate models for discretization-independent, continuous representations of PDE solutions, which can be used for learning and prediction over domains with complex, variable geometry and mesh topology. Three methods are proposed and compared; design-variable-coded multi-layer perceptron (DV-MLP), design-variable hypernetworks (DV-Hnet), and non-linear independent dual system (NIDS). Each method utilizes a main network which consumes pointwise spatial information to provide a continuous representation, allowing predictions at any location in the domain. Input features include a minimum-distance function evaluation to implicitly encode the problem geometry. The geometric design variables, which define and distinguish problem instances, are used differently by each method, appearing as additional main-network input features (DV-MLP), or as hypernetwork inputs (DV-Hnet and NIDS). The methods are applied to predict solutions around complex, parametrically-defined geometries on non-parametrically-defined meshes with model predictions obtained many orders of magnitude faster than the full order models. Test cases include a vehicle-aerodynamics problem with complex geometry and limited training data, with a design-variable hypernetwork performing best, with a competitive time-to-best-model despite a much greater parameter count.","url_abs":"https://arxiv.org/abs/2109.07018v4","url_pdf":"https://arxiv.org/pdf/2109.07018v4.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":"non-linear-independent-dual-system-nids-for","repo_url":"https://github.com/jamesduv/nids","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[{"method_slug":"hypernetwork","method_name":"HyperNetwork"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}