{"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/niert-accurate-numerical-interpolation","title":"NIERT: Accurate Numerical Interpolation through Unifying Scattered Data Representations using Transformer Encoder","arxiv_id":"2209.09078","date":"2022-09-19","proceeding":null,"authors":["Shizhe Ding","Boyang xia","Milong Ren","Dongbo Bu"],"abstract":"Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting excellent and generalizable performance. However, they still fall short in two aspects: \\textbf{1) inadequate representation learning}, resulting from separate embeddings of observed and target points in popular encoder-decoder frameworks and \\textbf{2) limited generalization power}, caused by overlooking prior interpolation knowledge shared across different domains. To overcome these limitations, we present a \\textbf{N}umerical \\textbf{I}nterpolation approach using \\textbf{E}ncoder \\textbf{R}epresentation of \\textbf{T}ransformers (called \\textbf{NIERT}). On one hand, NIERT utilizes an encoder-only framework rather than the encoder-decoder structure. This way, NIERT can embed observed and target points into a unified encoder representation space, thus effectively exploiting the correlations among them and obtaining more precise representations. On the other hand, we propose to pre-train NIERT on large-scale synthetic mathematical functions to acquire prior interpolation knowledge, and transfer it to multiple interpolation domains with consistent performance gain. On both synthetic and real-world datasets, NIERT outperforms the existing approaches by a large margin, i.e., 4.3$\\sim$14.3$\\times$ lower MAE on TFRD subsets, and 1.7/1.8/8.7$\\times$ lower MSE on Mathit/PhysioNet/PTV datasets. The source code of NIERT is available at https://github.com/DingShizhe/NIERT.","url_abs":"https://arxiv.org/abs/2209.09078v3","url_pdf":"https://arxiv.org/pdf/2209.09078v3.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":"niert-accurate-numerical-interpolation","repo_url":"https://github.com/dingshizhe/niert","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"},{"task_slug":"representation-learning","task_name":"Representation Learning"}],"methods":[{"method_slug":"mae","method_name":"MAE"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}