# Integrating Mechanistic and Data-Driven Models for Neurological Disorders through Differentiable Programming

arXiv: https://arxiv.org/abs/2606.06094 · HTML: https://mlsanity.com/paper/2606.06094/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 50 of its 132 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 30 of 50)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning](https://mlsanity.com/paper/2108.10470/) (2021)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Brax -- A Differentiable Physics Engine for Large Scale Rigid Body Simulation](https://mlsanity.com/paper/2106.13281/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [NeuralSim: Augmenting Differentiable Simulators with Neural Networks](https://mlsanity.com/paper/2011.04217/) (2020)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [On Second Order Behaviour in Augmented Neural ODEs](https://mlsanity.com/paper/2006.07220/) (2020)
- [TorchMD: A deep learning framework for molecular simulations](https://mlsanity.com/paper/2012.12106/) (2020)
- [The Elements of Differentiable Programming](https://mlsanity.com/paper/2403.14606/) (2024)
- [FluidLab: A Differentiable Environment for Benchmarking Complex Fluid Manipulation](https://mlsanity.com/paper/2303.02346/) (2023)
- [A Review of Differentiable Simulators](https://mlsanity.com/paper/2407.05560/) (2024)
- [Differentiability in Unrolled Training of Neural Physics Simulators on Transient Dynamics](https://mlsanity.com/paper/2402.12971/) (2024)
- [Dojo: A Differentiable Physics Engine for Robotics](https://mlsanity.com/paper/2203.00806/) (2022)
- [DaXBench: Benchmarking Deformable Object Manipulation with Differentiable Physics](https://mlsanity.com/paper/2210.13066/) (2022)
- [Differentiable Programming for Differential Equations: A Review](https://mlsanity.com/paper/2406.09699/) (2024)
- [Comprehensive Review of Neural Differential Equations for Time Series Analysis](https://mlsanity.com/paper/2502.09885/) (2025)
- [Learning Spatio-Temporal Model of Disease Progression with NeuralODEs from Longitudinal Volumetric Data](https://mlsanity.com/paper/2211.04234/) (2022)
- [DiffMimic: Efficient Motion Mimicking with Differentiable Physics](https://mlsanity.com/paper/2304.03274/) (2023)

## Abstract (arXiv)

Advances in computational modeling, neuroimaging, and artificial intelligence are revolutionizing the modeling of neurological disorders for improved diagnostics, prognosis, and treatment planning. Mechanistic models provide valuable scientific insight into the disorders, but in practice they are often simplified with assumptions or computationally expensive and slow to solve. However, while purely data driven approaches provide speed and scalability, they require large, high quality data to train and generally suffer from interpretability and generalization issues. This perspective paper presents a structured overview of hybrid modeling strategies, which combine deep learning models with physics based solvers, and are categorized into parallel, series, and parallel-series architectures. Three main approaches that have been emphasized are residual modeling for missing or incomplete physics, Neural Ordinary Differential Equations (NODEs) for continuous time dynamics approximation, and solver in the loop that accelerates traditional solvers with neural approximations. These hybrid models integrate the governing differential equation based formulations and deep learning to characterize the evolution of neurological disorders, and promise advanced personalized neurological modeling. In addition, the study explores and proposes different hybrid configurations to improve diagnosis accuracy, predict disease progression, and inform treatment strategies across a range of neurological disorders. These capabilities outperform standalone mechanistic or purely data driven approaches, making hybrid modeling a powerful tool, especially in applications involving modeling the progression and treatment responses in neurological conditions such as brain tumors, Alzheimer's disease, and stroke.