Implicit Neural Representations & Physics-Informed Neural Networks
Learning continuous neural function representations for complex signals and systems.
What are Implicit Neural Representations?
Implicit Neural Representations (INRs) model scientific data as continuous functions parameterized by neural networks. Rather than discretizing a field on a fixed mesh, an INR learns a mapping
$x \mapsto u_\theta(x)$,
allowing evaluation at arbitrary resolution while preserving differentiability with respect to inputs.
This function-space perspective enables resolution-independent modeling of high-dimensional physical fields, periodic signals, and parametric solution manifolds.
Publications
• Neural Functions for Learning Periodic Signal (ICLR 2025)
Proposed a neural function architecture tailored for learning periodic signals with improved extrapolation performance. Explicitly extracted periodic structure from measurements and incorporated it into the representation, addressing the overfitting and limited generalization of coordinate-based MLPs. Demonstrated strong performance on periodic differential equation solutions as well as real-world time series interpolation and forecasting tasks.
Authors: Woojin Cho, Minju Jo, KL, and Noseong Park
Paper: [Paper]
• PDEfuncta: Spectrally-Aware Neural Representation for PDE Solution Modeling (NeurIPS 2025)
Proposed Global Fourier Modulation (GFM) to mitigate spectral bias in implicit neural representations by injecting high-frequency structure at each layer. Introduced PDEfuncta, a meta-learning framework that enabled compact modeling of multiple solution fields and supported forward and inverse inference without retraining.
Authors: Minju Jo, Woojin Cho, Uvini Balasuriya Mudiyanselage, Seungjun Lee, Noseong Park, and KL
Paper: [Paper]
What are Physics-Informed Neural Networks?
Physics-Informed Neural Networks (PINNs) incorporate governing equations directly into the learning objective. Given a differential equation
\(\mathcal{F}(u) = 0,\)
a PINN minimizes both data mismatch and the PDE residual computed via automatic differentiation.
This framework enables mesh-free solution of forward and inverse problems while integrating physical constraints into neural function approximation.
Publications
• DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation (AAAI 2021)
Demonstrated that standard Physics-Informed Neural Networks (PINNs) struggle to extrapolate time-dependent nonlinear PDE solutions beyond the training domain. To address this limitation, introduced DPM, a new training strategy that significantly improves temporal extrapolation performance.
Authors: Jungeun Kim, KL, Dongeun Lee, Sheo Yon Jhin, and Noseong Park
Paper: [Paper]
• Hypernetwork-based Meta-Learning for Low-Rank Physics-Informed Neural Networks (NeurIPS 2023)
Introduced a hypernetwork-based meta-learning approach that generates low-rank physics-informed neural networks (PINNs) to efficiently solve parameterized PDEs. Improved computational efficiency and robustness while maintaining high accuracy across varying physical conditions.
Authors: Woojin Cho, KL, Donsub Rim, and Noseong Park
Paper: [Paper]
• Parameterized Physics-informed Neural Networks for Parameterized PDEs (ICML 2024)
Proposed Parameterized Physics-Informed Neural Networks (P²INNs), which incorporate latent parameter embeddings into PINNs to learn entire solution families of parameterized PDEs. Improved accuracy and generalization across varying parameter regimes compared to standard PINN approaches.
Authors: Woojin Cho, Minju Jo, Haksoo Lim, Kookjin Lee, Dongeun Lee, Sanghyun Hong, and Noseong Park
Paper: [Paper]