NTopo: Mesh-free Topology Optimization using Implicit Neural Representations
Jonas Zehnder, Yue Li, Stelian Coros, Bernhard Thomaszewski
Abstract
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.
Ask about this paper
Your agent reads all of it.
Lune indexed this paper to the last equation, along with the top-tier papers that cite it. Ask a question and the answer quotes them.
Cited by top-tier papers5
- Implicit Neural Spatial Representations for Time-dependent PDEsHonglin Chen, Rundi Wu, Eitan Grinspun, Changxi Zheng et al.ICML 2023 · 54 citations
- Neural Physical Simulation with Multi-Resolution Hash Grid EncodingHaoxiang Wang, Tao Yu, Tianwei Yang, Hui Qiao et al.AAAI 2024 · 10 citations
- Quaffure: Real-Time Quasi-Static Neural Hair SimulationTuur Stuyck, Gene Wei-Chin Lin, Egor Larionov, Hsiao-Yu Chen et al.CVPR 2025
- Feature-Mapping Topology Optimization with Neural Heaviside Signed Distance FunctionsAleksandr Kolomeitsev, Anh Huy PhanICML 2025
- GMT: A Geometric Multigrid Transformer Solver for Microstructure HomogenizationYu Xing, Yang Liu, Tianyang Xue, Lin LuSIGGRAPH 2026
Builds on8
- Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional DomainsMatthew Tancik, Pratul P. Srinivasan, Ben Mildenhall, Sara Fridovich-Keil et al.NeurIPS 2020 · 4,036 citations
- Implicit Neural Representations with Periodic Activation FunctionsVincent Sitzmann, Julien N. P. Martel, Alexander W. Bergman, David B. Lindell et al.NeurIPS 2020 · 4,008 citations
- Learning to Simulate Complex Physics with Graph NetworksAlvaro Sanchez-Gonzalez, Jonathan Godwin, Tobias Pfaff, Rex Ying et al.ICML 2020 · 1,439 citations
- Learning Mesh-Based Simulation with Graph NetworksTobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, Peter W. BattagliaICLR 2021 · 1,175 citations
- Learning to Control PDEs with Differentiable PhysicsPhilipp Holl, Nils Thuerey, Vladlen KoltunICLR 2020 · 221 citations
Related papers
- Meta-Learning Sparse Implicit Neural RepresentationsJaeho Lee, Jihoon Tack, Namhoon Lee, Jinwoo ShinNeurIPS 2021 · 60 citations
- Optimize Any Topology: A Foundation Model for Shape- and Resolution-Free Structural Topology OptimizationAmin Heyrani Nobari, Lyle Regenwetter, Cyril Picard, Ligong Han et al.NeurIPS 2025 · 6 citations
- MeshSDF: Differentiable Iso-Surface ExtractionEdoardo Remelli, Artem Lukoianov, Stephan R. Richter, Benoît Guillard et al.NeurIPS 2020 · 186 citations
- HyperDiffusion: Generating Implicit Neural Fields with Weight-Space DiffusionZiya Erkoç, Fangchang Ma, Qi Shan, Matthias Nießner et al.ICCV 2023 · 174 citations
- Inverse Design for Fluid-Structure Interactions using Graph Network SimulatorsKelsey R. Allen, Tatiana Lopez-Guevara, Kimberly L. Stachenfeld, Alvaro Sanchez-Gonzalez et al.NeurIPS 2022 · 37 citations
