# Recovering implicit physics model under real-world constraints

arXiv: https://arxiv.org/abs/2412.02215 · HTML: https://mlsanity.com/paper/2412.02215/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 12 of 12)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control](https://mlsanity.com/paper/2111.10992/) (2021)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Closed-form Continuous-time Neural Models](https://mlsanity.com/paper/2106.13898/) (2021)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [Explainable AI via Learning to Optimize](https://mlsanity.com/paper/2204.14174/) (2022)
- [Framework for developing and evaluating ethical collaboration between expert and machine](https://mlsanity.com/paper/2411.10983/) (2024)
- [Investigating Sindy As a Tool For Causal Discovery In Time Series Signals](https://mlsanity.com/paper/2212.14133/) (2022)
- [High Fidelity Fast Simulation of Human in the Loop Human in the Plant (HIL-HIP) Systems](https://mlsanity.com/paper/2309.06558/) (2023)

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

- [Accelerated Digital Twin Learning for Edge AI: A Comparison of FPGA and Mobile GPU](https://mlsanity.com/paper/2512.17941/) (2025)
- [Hardware Software Optimizations for Fast Model Recovery on Reconfigurable Architectures](https://mlsanity.com/paper/2512.06113/) (2025)
- [Enabling Physical AI at the Edge: Hardware-Accelerated Recovery of System Dynamics](https://mlsanity.com/paper/2512.23767/) (2025)
- [EMMA: Extracting Multiple physical parameters from Multimodal Data](https://mlsanity.com/paper/2605.24047/) (2026)

## Abstract (arXiv)

Recovering a physics-driven model, i.e. a governing set of equations of the underlying dynamical systems, from the real-world data has been of recent interest. Most existing methods either operate on simulation data with unrealistically high sampling rates or require explicit measurements of all system variables, which is not amenable in real-world deployments. Moreover, they assume the timestamps of external perturbations to the physical system are known a priori, without uncertainty, implicitly discounting any sensor time-synchronization or human reporting errors. In this paper, we propose a novel liquid time constant neural network (LTC-NN) based architecture to recover underlying model of physical dynamics from real-world data. The automatic differentiation property of LTC-NN nodes overcomes problems associated with low sampling rates, the input dependent time constant in the forward pass of the hidden layer of LTC-NN nodes creates a massive search space of implicit physical dynamics, the physics model solver based data reconstruction loss guides the search for the correct set of implicit dynamics, and the use of the dropout regularization in the dense layer ensures extraction of the sparsest model. Further, to account for the perturbation timing error, we utilize dense layer nodes to search through input shifts that results in the lowest reconstruction loss. Experiments on four benchmark dynamical systems, three with simulation data and one with the real-world data show that the LTC-NN architecture is more accurate in recovering implicit physics model coefficients than the state-of-the-art sparse model recovery approaches. We also introduce four additional case studies (total eight) on real-life medical examples in simulation and with real-world clinical data to show effectiveness of our approach in recovering underlying model in practice.