Boltzmann priors for Implicit Transfer Operators
Juan Viguera Diez, Mathias Schreiner, Ola Engkvist, Simon Olsson
TL;DR
This paper introduces BoPITO, a novel method that enhances Implicit Transfer Operator learning by improving data efficiency and embedding long-term dynamical biases, enabling more accurate and unbiased thermodynamic predictions in molecular simulations.
Contribution
BoPITO integrates Boltzmann priors into ITO learning, significantly improving sample efficiency and ensuring unbiased equilibrium statistics in molecular dynamics simulations.
Findings
Sample efficiency improved by an order of magnitude.
Guarantees asymptotically unbiased equilibrium statistics.
Enables tunable sampling between off-equilibrium and equilibrium models.
Abstract
Accurate prediction of thermodynamic properties is essential in drug discovery and materials science. Molecular dynamics (MD) simulations provide a principled approach to this task, yet they typically rely on prohibitively long sequential simulations. Implicit Transfer Operator (ITO) Learning offers a promising approach to address this limitation by enabling stable simulation with time steps orders of magnitude larger than MD. However, to train ITOs, we need extensive, unbiased MD data, limiting the scope of this framework. Here, we introduce Boltzmann Priors for ITO (BoPITO) to enhance ITO learning in two ways. First, BoPITO enables more efficient data generation, and second, it embeds inductive biases for long-term dynamical behavior, simultaneously improving sample efficiency by one order of magnitude and guaranteeing asymptotically unbiased equilibrium statistics. Furthermore, we…
Peer Reviews
Decision·ICLR 2025 Poster
- This method could enable running MD simulations over much longer timescales - By incorporating Boltzmann priors into the training process, this could allow more data efficiency and also ensure recovering the Boltzmann distribution over time
- There are many ways to do molecular dynamics simulations. A common way is through methods like machine learning potentials. While the time steps that are taken there are smaller, these potentials are much more accurate and have been used for more diverse systems. It would be helpful if the authors provided some comparison to this method, as well as other methods that also try to directly predict molecular dynamics. - The authors have only run this on two very toy systems: the 1D Prinz potenti
The paper applies Boltzmann generators in ITO models to capture modes that have very small probability mass in the Boltzmann distributions.
1. Pre-trained Boltzmann generator (BG) My main concern with this paper is that it assumes a pre-trained BG. Since BG is trained using the energy function and data samples (more detail in Q2), I am a bit confused about what the authors intended. Is BG only used to generate initial conditions for simulations, for various sampling across the configuration space? 2. Lack of detail of less extensive use of data compared to ITO One of the important limitations the authors pointed out was the need
- The paper is clearly written and easy to follow. Overall, it represents a pleasant read. - The authors made a great effort to make the paper self-contained, including a lot of background sections covering the basics of MD, BGs, ITOs, and diffusion models. - Numerical results are convincing in showing advantages compared to ITOs (PRO), although the approach is not compared to other baselines/methods in the literature (CON). This allows us to only partially appreciate the advantages of the alg
- I find the main weakness of this work being the lack of comparison with other ML-based approaches that can deal with sampling at different time scales (e.g., [3,4]). Moreover, it would also be useful to show a ground truth in the plots when possible, e.g., Fig. 5. Adding more baselines would certainly improve the manuscript. - As a suggestion, rather than a weakness, I feel it would be better to move the discussion to the related work at the beginning of the paper. This would help people to a
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Mathematical Biology Tumor Growth · Numerical methods in inverse problems