# Physics-informed reduced order model with conditional neural fields

arXiv: https://arxiv.org/abs/2412.05233 · HTML: https://mlsanity.com/paper/2412.05233/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 6 Dec 2024.

## Builds on (most cited first, 9 of 9)

- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Continuous PDE Dynamics Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2209.14855/) (2022)
- [CROM: Continuous Reduced-Order Modeling of PDEs Using Implicit Neural Representations](https://mlsanity.com/paper/2206.02607/) (2022)
- [Parameterized Physics-informed Neural Networks for Parameterized PDEs](https://mlsanity.com/paper/2408.09446/) (2024)
- [Evolve Smoothly, Fit Consistently: Learning Smooth Latent Dynamics For Advection-Dominated Systems](https://mlsanity.com/paper/2301.10391/) (2023)
- [Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equations](https://mlsanity.com/paper/2406.03919/) (2024)
- [Reduced-order modeling for parameterized PDEs via implicit neural representations](https://mlsanity.com/paper/2311.16410/) (2023)
- [FO-PINNs: A First-Order formulation for Physics Informed Neural Networks](https://mlsanity.com/paper/2210.14320/) (2022)

## Built on by (most cited first, 4 of 4)

- [A Physics-Informed Meta-Learning Framework for the Continuous Solution of Parametric PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2504.02459/) (2025)
- [Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers](https://mlsanity.com/paper/2505.14595/) (2025)
- [Architecture Shapes Transfer Specificity in Implicit Neural Representations](https://mlsanity.com/paper/2606.06827/) (2026)
- [Linearized PINN with pretrained nonlinear layers](https://mlsanity.com/paper/2609.14926/) (2026)

## Abstract (arXiv)

This study presents the conditional neural fields for reduced-order modeling (CNF-ROM) framework to approximate solutions of parametrized partial differential equations (PDEs). The approach combines a parametric neural ODE (PNODE) for modeling latent dynamics over time with a decoder that reconstructs PDE solutions from the corresponding latent states. We introduce a physics-informed learning objective for CNF-ROM, which includes two key components. First, the framework uses coordinate-based neural networks to calculate and minimize PDE residuals by computing spatial derivatives via automatic differentiation and applying the chain rule for time derivatives. Second, exact initial and boundary conditions (IC/BC) are imposed using approximate distance functions (ADFs) [Sukumar and Srivastava, CMAME, 2022]. However, ADFs introduce a trade-off as their second- or higher-order derivatives become unstable at the joining points of boundaries. To address this, we introduce an auxiliary network inspired by [Gladstone et al., NeurIPS ML4PS workshop, 2022]. Our method is validated through parameter extrapolation and interpolation, temporal extrapolation, and comparisons with analytical solutions.