Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces

Nicolaï Gouraud; Côme Cattin; Thomas Plé; Olivier Adjoua; Louis Lagardère; Jean-Philip Piquemal

physics.chem-phFeb 16, 2026

Faster Molecular Dynamics with Neural Network Potentials via Distilled Multiple Time-Stepping and Non-Conservative Forces

Authors: Nicolaï Gouraud, Côme Cattin, Thomas Plé, Olivier Adjoua, Louis Lagardère, Jean-Philip Piquemal

Organizations: Qubit Pharmaceuticals, Advanced Research Department, 75014 Paris, France · Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France

Abstract

Following our previous work (J. Phys. Chem. Lett., 2026, 17, 5, 1288-1295), we propose the DMTS-NC approach, a distilled multi-time-step (DMTS) strategy using non-conservative (NC) forces to further accelerate atomistic molecular dynamics simulations using foundation neural network models such as FeNNix-Bio1. There, a dual-level reversible reference system propagator algorithm (RESPA) formalism couples a target accurate conservative potential to a simplified distilled representation optimized for the production of non-conservative forces. Despite being non-conservative, the distilled architecture is designed to enforce key physical priors, such as equivariance under rotation and cancellation of atomic force components. These choices facilitate the distillation process and therefore improve drastically the robustness of simulation, significantly limiting abnormal discrepancies between the two models, thus achieving excellent agreement with the forces data. Overall, the DMTS-NC scheme is found to be more stable and efficient than its conservative counterpart with additional speedups reaching 15-30% over DMTS. Requiring no fine-tuning steps, it is easier to implement and can be pushed to the limit of the systems physical resonances to maintain accuracy while providing maximum efficiency. We obtain additional speedup by combining hydrogen mass repartitioning (HMR), High Hydrogen Friction (HHF) to further extended the largest timestep up to 10fs of our schemes while conserving stability and accuracy. As for DMTS, DMTS-NC is applicable to any neural network potential and can be applied to approaches that are computationally heavier than FeNNix-Bio1. We show a proof of principle applying the approach to the distillation of MACE-OFF23 with consequent speedups ranging from 3.66 to 5.64 compared to single timestep.

Figures & tables

	Number of atoms			Numerical
Integrator	648	4800	12000	instabilities
STS	$36.89$	$9.08$	$3.63$	No
DMTS 1-5fs	$69.54$	$30.17$	$11.95$	No
DMTS 1-6fs	$80.62$	$34.34$	NaN	Data holes
DMTS 1-7fs	NaN	NaN	NaN	—
DMTS-NC 1-5fs	$91.13$	$32.69$	$12.39$	No

Table 1: Simulation performances for bulk water systems, expressed in nanoseconds per day. In DMTS-NC, the stability limit is reached around an external time step of

\Delta=6.5

fs, after what resonances start to appear. In contrast, the main limitation the with the (generic) conservative model is the presence of “data holes” already at

\Delta=6

fs.

Panel of Figure 1 — Figure 1: Sampling properties of bulk water simulations. All data was collected from 2 nanosecond simulations, with one frame saved per picosecond. Figure (a) shows that radial distributions are not affected by the use of DMTS-NC compared to DMTS or STS, Figure (b) shows that temperatures fit the equilibrium theoretical distribution, and samples of potential energies, represented on a boxplot (Figure (c)) and a quantile-quantile plot (Figure (d)), highlight the low-bias identical-variance deviation of the distributions from STS to DMTS-NC, as expected for a multi-time-step method in a stable regime.

	Speed (ns/day)		Numerical
Integrator	Phenol-lyso.	DHFR	instabilities
STS	$2.55$	$1.85$	No
DMTS 1.75-3.5	$6.59$	$4.46$	No
DMTS 1-4	NaN	NaN	—
Fine-tuned DMTS 2-4	$7.45$	$4.97$	No
DMTS-NC 1-4	$7.20$	$4.89$	No

Table 2: Speed performances for the two ligand-protein systems. Similarly to bulk water simulations, DMTS-NC allows to use a larger external time step than conservative DMTS, without relying on active learning.

System		Integrator	Temperature	Potential energy
			(K)	(kcal/mol/atom)
Water boxes	216 mol.	STS	$299.84$ 9.57	$-8.049$ 0.042
		DMTS-NC	$299.87$ 9.56	$-8.038$ 0.043
	1600 mol.	STS	$300.09$ 3.60	$-8.047$ 0.017
		DMTS-NC	$299.93$ 3.54	$-8.037$ 0.016
	4000 mol.	STS	$300.61$ 2.93	$-8.043$ 0.014

Table 3: Average temperatures and potential energies (

\pm

empirical standard deviations). DMTS-NC simulations were performed at the highest stable time steps that we found, i.e.

\delta=1.25

fs–

\Delta=5

fs for the protein systems, and

\delta=1.2

fs–

\Delta=6

fs for bulk water.

Panel of Figure 2 — Figure 2: Time evolution of the protein backbone RMSD (Figure (a)) and the ligand’s Distance to Bound Configuraiton (Figure (b)) during a 20ns simulation of the solvated lysosyme-phenol. The DMTS-NC integrator uses $\delta=1.25$ fs– $\Delta=5$ fs time steps.

Figure 3: Hydration free energy of 44 small molecules in NPT. Error bars are computed from three independent lambda-ABF runs for each integrator and each molecule.

		Water boxes		Solvated prot.
System size / Name		1600 mol.	4000 mol.	Phenol-Lys.	DHFR
Speed (ns/day)	STS 1 fs	9.08	3.63	2.55	1.85
	DMTS-NC	36.2	13.7	8.42	5.57
	HHF	47.9	17.2	9.09	6.38
HHF Accel. w.r.t.	DMTS-NC	32.61 $\%$	25.92 $\%$	7.96 $\%$	14.57 $\%$
HHF Accel. w.r.t.	STS	5.28	4.74	3.56	3.45

Table 4: HHF speed performances and acceleration compared to DMTS-NC and STS.

System		Time steps	Temperature	Pot. Energy (kcal/mol/atom)
		(fs)	(K)	DMTS-NC	STS
Water boxes	1600 mol.	1–10	$300$ 4	$-8.02$ 0.02	$-8.05$ 0.02
Water boxes	4000 mol.	1–10	$300$ 2	$-8.02$ 0.01	$-8.04$ 0.01
Solvated prot.	Phenol-Lys.	1–6	$297$ 2	$-7.87$ 0.01	$-7.87$ 0.01
Solvated prot.	DHFR	1–7	$298$ 2	$-7.81$ 0.01	$-7.82$ 0.01

Table 5: HHF average temperatures and potential energies.

System size / Name		216 mol.	1600 mol.	4000 mol.	Phenol-Lys.	DHFR
		Water boxes			Solvated prot.
Speed (ns/day)	STS	7.40	1.04	0.38	0.31	0.22
Speed (ns/day)	DMTS-NC	37.59	5.88	2.07	1.14	1.00
Acceleration		5.08	5.64	5.45	3.66	4.62

Table 6: DMTS-NC performances with MACE-OFF23(S).

Figure 4: Hydrogen velocity auto-correlation spectra for various external time steps, in a system of 1600 water molecules. From left to right, the first peak corresponds to molecule libration and slow fluctuations in the hydrogen bond network, the second peak to angle bending oscillations and the third and fourth peaks to bond stretching motions. The ones on the inset graph are non-physical artifacts. As the external time step increases, these peaks shift to the left, eventually coupling with the bond-oscillation peak at the stability limit.

Panel of Figure 5 — Figure 5: Mean-square displacement (Figure (a)) and diffusion coefficients (Figure (b)) for various time steps and thermostats.

Integrator	Diffusion coeff. (Å 2 /ps)	Loss w.r.t. STS (%)
STS	$0.1672$ 0.0017	—
STS-HMR	$0.1472$ 0.0012	$12.0$
DMTS 1-5	$0.1525$ 0.0007	$8.8$
DMTS-NC 1-6	$0.1461$ 0.0005	$12.6$
HHF 1-10 Langevin	$0.1016$ 0.0003	$39.2$
HHF 1-10 FFL	$0.1126$ 0.0007	$32.6$

Table 7: Diffusion coefficients for various MTS strategies. The loss represents the relative decrease in diffusion compared to the STS reference.

Molecular Dynamics Simulation

Molecular dynamics simulation models atomic motion to study molecular structure, material behavior, reactions, and thermodynamic properties.

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