Machine learning interatomic potentials for molecular dynamic simulations: are they good?

Question

I know the general question of machine learning in computational chemistry has been already raised here: What is the current status of machine learning applied to materials or molecular systems?

However, still, I'm curious, what are the pros and cons of ML force fields for MD simulations.

Classical empirical potential models are fast but they are incorrect or cannot predict specific chemistry and bond formation/dissociation. Reactive potentials have some accuracy (depending on parameters) but they are slow.

Then... where is the position of ML potentials? Are they accurate? Or fast? Or both? I read some papers by Podryabinkin et. al.^[1] and by Deringer et al..^[2]

However, as a person who never tried ML potentials before, it is really hard to judge or feel the state of the ML force field.

So, if anyone tried various interatomic potentials including ML force fields (in Gromacs or Lammps or any platforms) may I ask how much accurate/fast are they, and what is the advantage/disadvantage of ML force field? Is this easy/hard to learn, or easy/hard to get "good parameter", etc..

References:

1. Podryabinkin, E. V.; Tikhonov, E. V.; Shapeev, A. V.; Oganov, A. R. Accelerating crystal structure prediction by machine-learning interatomic potentials with active learning. Phys. Rev. B 2019, 99 (6), No. 064114. DOI: 10.1103/PhysRevB.99.064114.
2. Deringer, V. L.; Caro, M. A.; Csányi, G. Machine Learning Interatomic Potentials as Emerging Tools for Materials Science. Adv. Mater. 2019, 31 (46), 1902765. DOI: 10.1002/adma.201902765.

Answer 1

(Expanding my comment into an answer) When ML-based forcefields are compared to classical forcefield directly, I think we miss the most important points. ML-based models have several advantages:

• They do not need an a priori "correct" description of the system, nor are they limited by the applicability of specific theories to your system. Classical force fields are very sophisticated for problems like biological molecules or water simulation, but once you start simulating transition metal compounds or their oxides, suddenly you have to invent new types of forcefields. ML-based models are flexible; you do not have to invent it every single time. Also, they are flexible in the sense that their accuracy is not limited by the model you choose: it is possible to improve their accuracy by training them on more data.

Therefore, theoretically, one can reach CCSD(T) or whatever level of accuracy if enough data is previously collected [1].

• We generally know (and measure) the errors. It is not really a theoretical limitation, but as far as I know, MM software like Gromacs or NAMD is not telling you when your system is far from the training set.

Why is it important? We can do things like new forcefields on the fly: one can start an MD simulation with DFT, and parallel train a forcefield. Continue the simulation with ML-forcefield and calculate DFT only when something new is happening (a structure that is far from the training set)[2].

Are they slow compared to a GROMACS force field? Yes. But it is mostly irrelevant in cases where there is no classic force field at all or where more accuracy is needed or when you speed up a QM-MD simulation x100...0(?) times.

1. Smith, J.S., Nebgen, B.T., Zubatyuk, R. et al. "Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning." Nat Commun 10, 2903 (2019). DOI: 10.1038/s41467-019-10827-4
2. Vasp.at. 2020. Machine Learning Force Field: Theory - Vaspwiki. [online] Available at: https://www.vasp.at/wiki/index.php/Machine_learning_force_field:_Theory [Accessed 18 May 2020]

Answer 2

Before talking about the pros and cons of ML-potentials, there is a huge conceptual difference between empirical- and ML-potential that needs to be clarified.

In empirical potentials, one uses data from experiments to find the parameters of a fixed functional form that would explain the experiment. This is an inverse problem which is mathematically ill-posed (in the sense of Hadamard).

However, ML-potentials are not posed as an inverse problem. Here, in the framework of Potential Energy Surfaces (PES), one starts by selecting a set of distinct nuclear geometries, compute their energies using some quantum chemistry method. Then, the PES is obtained by solving a regression problem, where one seeks to minimise the empirical risk functional.

The point is, the two approaches are conceptually very different.

where is the position of ML potentials? Are they accurate? Or fast? Or both?

Depends on the model you use to solve the regression problem. You can use Neural Networks, Kernel-methods, or even polynomial fitting. These methods differ from each other in terms of training complexity, prediction complexity and their ability to approximate highly nonlinear functions. A wide variety of algorithms have been successfully used to obtain PESs.

Is this easy/hard to learn?

It depends on the quality of your data and the algorithm you're using. But, in general, developing any ML-model is an iterative procedure (candidate model-train-test).