# Physics Encoded Blocks in Residual Neural Network Architectures for Digital Twin Models

arXiv: https://arxiv.org/abs/2411.11497 · HTML: https://mlsanity.com/paper/2411.11497/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 18 Nov 2024.

## Builds on (most cited first, 20 of 20)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Digital Twin: Values, Challenges and Enablers](https://mlsanity.com/paper/1910.01719/) (2019)
- [Propagation Networks for Model-Based Control Under Partial Observation](https://mlsanity.com/paper/1809.11169/) (2018)
- [A Point-Cloud Deep Learning Framework for Prediction of Fluid Flow Fields on Irregular Geometries](https://mlsanity.com/paper/2010.09469/) (2020)
- [Augmenting Physical Simulators with Stochastic Neural Networks: Case Study of Planar Pushing and Bouncing](https://mlsanity.com/paper/1808.03246/) (2018)
- [A Phase Shift Deep Neural Network for High Frequency Approximation and Wave Problems](https://mlsanity.com/paper/1909.11759/) (2019)
- [Enforcing Statistical Constraints in Generative Adversarial Networks for Modeling Chaotic Dynamical Systems](https://mlsanity.com/paper/1905.06841/) (2019)
- [A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies](https://mlsanity.com/paper/2208.14197/) (2022)

## Built on by (most cited first, 1 of 1)

- [AgenticTwin: An Agentic LLM Framework Integrated with Digital Twin for Anomaly Detection](https://mlsanity.com/paper/2608.11679/) (2026)

## Abstract (arXiv)

Physics Informed Machine Learning has emerged as a popular approach for modeling and simulation in digital twins, enabling the generation of accurate models of processes and behaviors in real-world systems. However, existing methods either rely on simple loss regularizations that offer limited physics integration or employ highly specialized architectures that are difficult to generalize across diverse physical systems. This paper presents a generic approach based on a novel physics-encoded residual neural network (PERNN) architecture that seamlessly combines data-driven and physics-based analytical models to overcome these limitations. Our method integrates differentiable physics blocks-implementing mathematical operators from physics-based models with feed-forward learning blocks, while intermediate residual blocks ensure stable gradient flow during training. Consequently, the model naturally adheres to the underlying physical principles even when prior physics knowledge is incomplete, thereby improving generalizability with low data requirements and reduced model complexity. We investigate our approach in two application domains. The first is a steering model for autonomous vehicles in a simulation environment, and the second is a digital twin for climate modeling using an ordinary differential equation (ODE)-based model of Net Ecosystem Exchange (NEE) to enable gap-filling in flux tower data. In both cases, our method outperforms conventional neural network approaches as well as state-of-the-art Physics Informed Machine Learning methods.