# What are the advantages of (semi)-empirical force fields over Machine Learning Potentials?

I am currently working with ReaxFF, an empirical reactive force field that can describe chemical bond forming and breaking. The main advantage over ab initio methods are of course the greatly increased system and time scales, with the drawback of inferior accuracy.

Recently, machine learning potentials have introduced themselves as methods that are much cheaper to calculate than ab initio methods, but with almost on-par accuracy.

A few months back, one could argue that empirical force fields are still considerably faster than MLP's. Another typical argument was that much less training data was required to refit a force field than to train a MLP. However, the recent developments in MLP's (for example NequIP) are countering all those arguments, as the speed is currently very close, accuracy is much better and the required training set size is decreasing quickly.

Is there still an objective argument to justify the use and further development of empirical force fields in a time of machine learning potentials?

• Some interesting discussion in the comments, but it was starting to get long. I have moved all the comments to one our chatrooms where you can continue to discuss this.
– Tyberius
Feb 28 at 14:48

The answer to this question is inevitably going to be opinionated. My opinion is that there are still very good reasons to explore the development of force fields while also pursuing better ML potentials. Here is a list of reasons I think force fields are worth pursuing.

Points in Favor of Force Fields:

• Interpretation of the fidelity of force fields is straightforward. Most importantly, it is fairly easy to understand the limitations of a model you fit with physically meaningful parameters
• Force fields, in principle, should be faster than ML potentials because they inevitably require less computation. In practice, I'm not sure this is going to be the case because it's hard to write efficient GPU code by hand and hence tons of parallelization is left on the table
• Force fields are easier to distribute and use than ML potentials (this might be a contentious point)
• Certain types of force fields can be made exceptionally accurate with minimal electronic structure calculations (e.g. see MB-UCB which is a very accurate water model using only calculations up to the water pentamer)
• This is a meta-reason that I still think is important: scientists learn things about phsyics/chemistry/materials from making a force field. Fitting an ML force field mostly teaches you about computer science.
• Expanding a force field to include new atoms is often quite straightforward and shouldn't make the existing potential worse. That is, adding an atom to ReaxFF only involves fitting a dozen-ish new paramaters. This is not at all the case for an ML potential because re-training with new data might actually make the existing potential worse, which effectively creates a "version control" problem for reproducing past science. It's not clear how much of a problem that really is though.

Points in Favor of ML Potentials:

• The accuracy is almost certainly going to be better with ML potentials in general. Note that this is true somewhat trivially. ML potentials use many orders of magnitude more parameters than force fields, so they better be more accurate. Also, one could argue that ML potentials aren't necessarily always going to be more accurate. This is because they are often restricted to DFT-based methods and many existing force fields are more accurate than DFT for specific systems.

• You get a GPU-based potential "for free". This, in my mind, is actually the biggest selling point for ML potentials. Scientists always want larger, better models to simulate, and ML force fields give you parallelism for free since all the infrastructure of ML already runs on GPUs.

• ML force fields can be bootstrapped to become more accurate. I'm thinking of recent $$\Delta$$-ML models where a cheaper method is used to generate a full force field and then a smaller sample of configurations is used to correct this model to a higher-accuracy method. There's not an obvious parallel to this for force fields.

Here is the biggest problem restricting machine learning potentials from taking over. Fitting a generic machine learned potential is almost entirely a sampling problem, and there is an infinite amount of chemical space that needs to be sampled. Many-body expansion techniques avoid this problem by limiting the search to small sub-systems. This then introduces a problem of combinatorial complexity in how many atoms can be included in the model. MOB-ML circumvents the combinatorial explosion of atom-types by fitting to orbital information. The downside of this is that it requires orbitals and hence MOB-ML calculations are slow.

Basically, ML is greedy for data. The mechanics of how to fit force fields is actually quite well understood at this point. So, people are going to need molecular configurations. A lot of these configurations are going to come from force fields, which then get labelled using electronic structure.

I'm sure there are tons of points on both sides I missed, as I wrote this somewhat stream of consciousness. The reality is that people will work on both sides of things (I personally am working on both sides of this). This is good. The two techniques can and will feed off of each other. For instance, doing $$\Delta$$-ML off of relatively crude force fields seems like a possibly useful idea.

• Thanks a lot for the comparison! There are many arguments that I didn't consider. I was just wondering if you could elaborate a bit more on your last sentence? Am I correct that you use force fields to generate structures to do Δ-ML on them? Mar 2 at 13:26
• @Icdumont I haven't personally done this, but it has been done using DFTB methods and then refined using coupled-cluster. I don't see any reason this wouldn't be possible with pure force field methods. I haven't seen that done yet though. Mar 2 at 17:55