# Learning Physics Informed Neural ODEs With Partial Measurements

arXiv: https://arxiv.org/abs/2412.08681 · HTML: https://mlsanity.com/paper/2412.08681/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 50 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Practical Quasi-Newton Methods for Training Deep Neural Networks](https://mlsanity.com/paper/2006.08877/) (2020)
- [Discovering Governing Equations from Partial Measurements with Deep Delay Autoencoders](https://mlsanity.com/paper/2201.05136/) (2022)
- [Neural ODE Processes](https://mlsanity.com/paper/2103.12413/) (2021)
- [Heavy Ball Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.04840/) (2021)
- [Stochastic Block BFGS: Squeezing More Curvature out of Data](https://mlsanity.com/paper/1603.09649/) (2016)
- [Scalable Second Order Optimization for Deep Learning](https://mlsanity.com/paper/2002.09018/) (2020)
- [Differentiable Multiple Shooting Layers](https://mlsanity.com/paper/2106.03885/) (2021)
- [Recognition Models to Learn Dynamics from Partial Observations with Neural ODEs](https://mlsanity.com/paper/2205.12550/) (2022)
- [Efficient Modeling of Morphing Wing Flight Using Neural Networks and Cubature Rules](https://mlsanity.com/paper/2110.01057/) (2021)

## Built on by (most cited first, 9 of 9)

- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [PILD: Physics-Informed Learning via Diffusion](https://mlsanity.com/paper/2601.21284/) (2026)
- [Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimation](https://mlsanity.com/paper/2502.20772/) (2025)
- [Recovering Physical Dynamics from Discrete Observations via Intrinsic Differential Consistency](https://mlsanity.com/paper/2605.08454/) (2026)
- [Learning Hybrid Biophysical Neuron Models with Neural ODEs](https://mlsanity.com/paper/2606.16693/) (2026)
- [Recursive Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/2504.13241/) (2025)
- [Learning partially observed systems with neural Hamiltonian ordinary differential equations](https://mlsanity.com/paper/2605.23510/) (2026)
- [RTS Smoother-Guided Learning of Physics-Based Neural Differential Models](https://mlsanity.com/paper/2607.15180/) (2026)
- [Retracing Hodgkin and Huxley: State Recovery Does Not Certify Mechanism](https://mlsanity.com/paper/2609.34566/) (2026)

## Abstract (arXiv)

Learning dynamics governing physical and spatiotemporal processes is a challenging problem, especially in scenarios where states are partially measured. In this work, we tackle the problem of learning dynamics governing these systems when parts of the system's states are not measured, specifically when the dynamics generating the non-measured states are unknown. Inspired by state estimation theory and Physics Informed Neural ODEs, we present a sequential optimization framework in which dynamics governing unmeasured processes can be learned. We demonstrate the performance of the proposed approach leveraging numerical simulations and a real dataset extracted from an electro-mechanical positioning system. We show how the underlying equations fit into our formalism and demonstrate the improved performance of the proposed method when compared with baselines.