# Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations

arXiv: https://arxiv.org/abs/2601.22328 · HTML: https://mlsanity.com/paper/2601.22328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 59 references that are in the map.
- First posted on arXiv 29 Jan 2026.

## Builds on (most cited first, 16 of 16)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Interpretable Scientific Discovery with Symbolic Regression: A Review](https://mlsanity.com/paper/2211.10873/) (2022)
- [Symbolic Regression is NP-hard](https://mlsanity.com/paper/2207.01018/) (2022)
- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Integrating Expert ODEs into Neural ODEs: Pharmacology and Disease Progression](https://mlsanity.com/paper/2106.02875/) (2021)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Discovering Sparse Interpretable Dynamics from Partial Observations](https://mlsanity.com/paper/2107.10879/) (2021)
- [Neural Laplace: Learning diverse classes of differential equations in the Laplace domain](https://mlsanity.com/paper/2206.04843/) (2022)
- [Training Neural Networks is NP-Hard in Fixed Dimension](https://mlsanity.com/paper/2303.17045/) (2023)
- [Neural Dynamical Systems: Balancing Structure and Flexibility in Physical Prediction](https://mlsanity.com/paper/2006.12682/) (2020)
- [OccamNet: A Fast Neural Model for Symbolic Regression at Scale](https://mlsanity.com/paper/2007.10784/) (2020)
- [Physics-informed kernel learning](https://mlsanity.com/paper/2409.13786/) (2024)
- [Symbolic Regression on Sparse and Noisy Data with Gaussian Processes](https://mlsanity.com/paper/2309.11076/) (2023)
- [No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs](https://mlsanity.com/paper/2501.18563/) (2025)

## Abstract (arXiv)

Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories. Instead, measurements are often partial, noisy, and heterogeneous, providing fragmented views of latent dynamical states. We introduce MAAT (Model Aware Approximation of Trajectories), a framework for knowledge-informed Kernel State Reconstruction in partially observed dynamical systems. MAAT formulates reconstruction in a reproducing kernel Hilbert space and incorporates heterogeneous observation operators together with semantic and structural priors, including non-negativity, conservation constraints, and domain-specific measurement models. This yields smooth, physically consistent state estimates with analytic time derivatives, providing a principled interface between fragmented measurements and downstream mechanistic discovery methods such as symbolic regression. Across nine scientific benchmarks, multiple noise regimes, and a real-world COVID-19 dataset, MAAT substantially reduces trajectory and derivative reconstruction error relative to strong baselines.