NeurIPS 2025

PDEfuncta: Spectrally-Aware Neural Representation
for PDE Solution Modeling
Minju Jo1∗
Woojin Cho2∗
Uvini Balasuriya Mudiyanselage3
Seungjun Lee4
Noseong Park5
Kookjin Lee3†
1Sorbonne University,
2TelePIX,
3SCAI, Arizona State University,
4Brookhaven National Laboratory,
5KAIST
minnju42@gmail.com, woojin.py@gmail.com, ubalasur@asu.edu,
slee19@bnl.gov, noseong@kaist.ac.kr, kookjin.lee@asu.edu
Abstract
Scientific machine learning often involves representing complex solution fields that
exhibit high-frequency features such as sharp transitions, fine-scale oscillations,
and localized structures. While implicit neural representations (INRs) have shown
promise for continuous function modeling, capturing such high-frequency behavior
remains a challenge—especially when modeling multiple solution fields with a
shared network. Prior work addressing spectral bias in INRs has primarily focused
on single-instance settings, limiting scalability and generalization. In this work,
we propose Global Fourier Modulation (GFM), a novel modulation technique that
injects high-frequency information at each layer of the INR through Fourier-based
reparameterization. This enables compact and accurate representation of multiple
solution fields using low-dimensional latent vectors. Building upon GFM, we
introduce PDEfuncta, a meta-learning framework designed to learn multi-modal
solution fields and support generalization to new tasks. Through empirical studies
on diverse scientific problems, we demonstrate that our method not only improves
representational quality but also shows potential for forward and inverse inference
tasks without the need for retraining.
1
Introduction
Solving partial differential equations (PDEs) is essential to progress in many science and engineering
applications, including fluid dynamics, seismic inversion, climate modeling, and mechanical design.
Traditionally, these PDE problems are addressed using numerical methods (e.g. finite-difference [1],
finite-volume [2], fi...