# Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields

arXiv: https://arxiv.org/abs/2208.12104 · HTML: https://mlsanity.com/paper/2208.12104/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 65 references that are in the map.
- First posted on arXiv 25 Aug 2022.

## Builds on (most cited first, 26 of 26)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Machine Learning of Linear Differential Equations using Gaussian Processes](https://mlsanity.com/paper/1701.02440/) (2017)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [Machine learning for molecular simulation](https://mlsanity.com/paper/1911.02792/) (2019)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Density Estimation in Infinite Dimensional Exponential Families](https://mlsanity.com/paper/1312.3516/) (2013)
- [Linearly constrained Gaussian processes](https://mlsanity.com/paper/1703.00787/) (2017)
- [Gauge equivariant neural networks for quantum lattice gauge theories](https://mlsanity.com/paper/2012.05232/) (2020)
- [Scaling Gaussian Process Regression with Derivatives](https://mlsanity.com/paper/1810.12283/) (2018)
- [Nonparametric Score Estimators](https://mlsanity.com/paper/2005.10099/) (2020)
- [High-Dimensional Gaussian Process Inference with Derivatives](https://mlsanity.com/paper/2102.07542/) (2021)
- [Linearly Constrained Gaussian Processes with Boundary Conditions](https://mlsanity.com/paper/2002.00818/) (2020)
- [Probabilistic Numeric Convolutional Neural Networks](https://mlsanity.com/paper/2010.10876/) (2020)
- [Symmetric and antisymmetric kernels for machine learning problems in quantum physics and chemistry](https://mlsanity.com/paper/2103.17233/) (2021)

## Built on by (most cited first, 7 of 7)

- [Hessian QM9: A quantum chemistry database of molecular Hessians in implicit solvents](https://mlsanity.com/paper/2408.08006/) (2024)
- [Transfer learning for atomistic simulations using GNNs and kernel mean embeddings](https://mlsanity.com/paper/2306.01589/) (2023)
- [Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence](https://mlsanity.com/paper/2212.12737/) (2022)
- [Stress and heat flux via automatic differentiation](https://mlsanity.com/paper/2305.01401/) (2023)
- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)
- [Scaling up machine learning-based chemical plant simulation: A method for fine-tuning a model to induce stable fixed points](https://mlsanity.com/paper/2307.13621/) (2023)
- [A Tutorial Review of Bayesian Optimization with Gaussian Processes to Accelerate Stationary Point Searches](https://mlsanity.com/paper/2603.10992/) (2026)

## Abstract (arXiv)

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process -- effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems -- all of high value to the FF community -- but also the simple inclusion of further physical knowledge such as higher-order information (e.g. Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.