ad-kernels

This repository contains the reference implementation of the article:

Algorithmic Differentiation for Automatized Modelling of Machine Learned Force Fields
Niklas Frederik Schmitz, Klaus-Robert Müller, Stefan Chmiela
The Journal of Physical Chemistry Letters 2022 13 (43), 10183-10189
Paper (open access) / ArXiv  / BibTeX

Speedups

Even on the small molecules of the MD17 data set, we observe practical relative speedups up to 50x for force prediction timings using our efficient higher-order AD contraction approach over naive dense higher-order AD:

	Ethanol (N=9)			Aspirin (N=21)
	dense	contraction	speedup	dense	contraction	speedup
sGDML	00.0780	0.0018	43.3x	000.2832	00.0087	x32.5
FCHL19GPR	57.9439	0.9815	59.0x	414.0216	10.1438	x40.8
sGDML[RBF]	00.0800	0.0015	53.3x	000.2811	00.0074	x37.9
global-FCHL19	57.5194	0.9653	59.5x	458.5465	10.0728	x45.5
sFCHL19	60.3951	1.0704	56.4x	419.3778	10.3336	x40.5

Benchmarked force prediction times (s) for different kernels. Each model was trained with 1000 training points, and evaluated for 10 points at the same time. All timings are averaged over 10 runs (excluding an initial run for just-in-time compilation). Our approach (contraction) yields consistent speedups by a up to two orders of magnitude over the direct (dense) implementation of the constrained models. All measurements are done on a single Nvidia Titan RTX 24 GB GPU.

See our article for details of where such speedups come from when considering algorithmic choices of higher-order AD and operator-transformed Gaussian processes.

Content

1. md17/
   • gdml_jax
     • a small toolbox focused on gradients and molecular force fields
   • train_sgdml.py
     • code for fitting different models to MD17 forces
   • experiments/schnetkernel
     • utils for schnetpack interop
   • hyper_coulomb.py
     • example on efficiently optimizing kernel hyperparameters by another outer level of AD
   • benchmark_forces.py
     • benchmark for dense instantiation vs fast operator kernel contraction
2. pde/ more general differential operators (gradients, Hessians, VJP, ...)
   • opgp_demo.ipynb
     • A 2D regession problem using gradients and Hessians
   • laplace.ipynb
     • A toy example solving Laplace's equation on an annulus
   • wave_eq.ipynb
     • A toy example solving a wave equation in one dimension

Requirements

• python 3.8
• JAX

Below is an example setup:

conda create -n ad-kernels python=3.8
conda activate ad-kernels
cd md17 && pip install -e .

Citation

@article{schmitz2022,
	title        = {Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields},
	author       = {Schmitz, Niklas Frederik and M\"uller, Klaus-Robert and Chmiela, Stefan},
	year         = 2022,
	journal      = {The Journal of Physical Chemistry Letters},
	volume       = 13,
	number       = 43,
	pages        = {10183--10189},
	doi          = {10.1021/acs.jpclett.2c02632},
	url          = {https://doi.org/10.1021/acs.jpclett.2c02632},
	eprint       = {https://doi.org/10.1021/acs.jpclett.2c02632}
}