Introducing Langevin Flow Maps TLDR: Neural Network Potentials that learn their own stochastic pathwise solution for faster simulation. - Transferable across molecular systems. - Transition dynamics are preserved. - No trajectory data are required. Work together with Sam McCallum, supervised by Alex Tong, and James Foster. Arxiv: Data: Code:

Machine Learning Force Fields (MLFFs) are fast and accurate potential energy functions, however, using them to run molecular simulations remains a challenge: (1) although fast for their level of accuracy, they are still slower than common molecular mechanics forcefields, and (2) many MLFFs encounter instabilities during simulation which are not explained by accuracy, symmetry, or energy conservation alone, coining the term "forces are not enough".

In order to improve the simulation throughput and stability of MLFF, we propose Langevin Flow Maps (LFMs): An auxiliary objective during training in which the model, conditioned on an additional time step size, and polynomial approximation of a Brownian path learns to predict the forces and velocities at a future state under Langevin dynamics.

For this we're building on our previous work on Strong Stochastic Flow Maps, which learn the pathwise solution of a Stochastic Flow Map using a semigroup objective To apply this approach to underdamped molecular dynamics, the flow map is predicting both forces and velocities at a future state.

Just like with Hamiltonian Flow Maps, Langevin Flow Maps can be trained with individual conformers only - they do not require trajectories of multiple timepoints for training. What excites us about the approach is that LFMs also learn the transition kinetics of smaller molecular systems, such as their mean first passage times.

A machine learning force field is most useful if it can generalize across unseen molecular system. We therefore trained a transferable LFM on a variety of oligopeptides.

We observe fast coverage of metastable states across unseen peptides for larger step sizes and similar performance to Amber14 BAOAB (our reference potential & integrator) for small steps. This gives us a knob to trade mode coverage for energetic fidelity.

In fact, LFMs even sample some missing modes in our benchmark dataset, which we validate with independent MD.

There is still work left to do. Right now we're only reaching simulation time/wall clock time parity with classical molecular mechanics for large steps and relatively small molecular systems. Enabling our model to (a) scale more efficiently with increasing atom count while taking (b) larger steps with (c) lower error remains an open challenge.

Tagging people that might be interested @FrankNoeBerlin @RipkenWinfried @michaelplainer @FrankThorben @kabylda_ @majdi_has @k_neklyudov @jchodera @HighSpeedMode @olexandr @TimothyDuignan @CorinWagen @AriWagen @PatrickKidger @smnlssn @SimonDBarnett @jgodwin_ai @StefanoErmon @jaschasd @sedielem @DidiKieran @karsten_kreis @RickyTQChen @emiel_hoogeboom @wellingmax @ValentinDeBort1 @nmboffi @PPotaptchik @msalbergo @mmbronstein @peholderrieth @HannesStaerk @GabriCorso

@sgmccallum @AlexanderTong7 @JamesFosterBath Any thoughts on extending this to explicit solvent simulations?

The biggest systems we’ve simulated so far are at the ca. 200 atom mark. To move towards 1000 atoms (solute + reasonable water box) we need to work out a way to scale the model more efficiently than its current implementation. There is precedent for this in NNPs obviously, so I am optimistic.

@sgmccallum @AlexanderTong7 @JamesFosterBath Very cool stuff! I'm wondering what the relation is to the original formulation of variational path sampling (

@sgmccallum @AlexanderTong7 @JamesFosterBath Thank you! At a first glance there seem to be a couple differences: We focus on equilibrium systems only and learn only the stochastic integrals to take larger steps. No biasing potentials and no focus on observing rare events per se. Hope that helps!

@sgmccallum @AlexanderTong7 @JamesFosterBath Incredible work Niklas! You're a force :)

@sgmccallum @AlexanderTong7 @JamesFosterBath Thank you James!

@sgmccallum @AlexanderTong7 @JamesFosterBath Great work! Excited to see applications of SSFMs in physical time

@sgmccallum @AlexanderTong7 @JamesFosterBath Amazing :)

@sgmccallum @AlexanderTong7 @JamesFosterBath Thank you Oscar :)

@sgmccallum @AlexanderTong7 @JamesFosterBath Congrats Niklas. Looks like nice work. Looking forward to follow how far you can push this idea.