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Tiwary, Pratyush

Publications and source records attributed to Tiwary, Pratyush.

A graph neural network-state predictive information bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics

Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. Here, in this work, we present a Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the state predictive information bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.

Zou, Ziyue↗

Simulating Crystallization in a Colloidal System Using State Predictive Information Bottleneck Based Enhanced Sampling

Here, we investigate crystal nucleation in supersaturated colloid suspensions using enhanced molecular dynamics simulations augmented with machine learning techniques. The simulations reveal that crystallization in the model colloidal system studied here, with particles interacting through a repulsive screened Coulomb Yukawa potential, proceeds from vapor to dense liquid droplet to crystalline phases across multiple high barriers. Employing a one-dimensional reaction coordinate derived from the State Predictive Information Bottleneck framework, our simulations capture back-and-forth phase transitions across multiple barriers effectively in biased metadynamics simulations. We obtain relative free energy differences between different phases and also quantify the roles of different molecular level features in driving the phase changes.

Chemistry↗

Modeling prebiotic chemistries with quantum accuracy at classical costs

Molecular Dynamics (MD) simulations using classical force-fields are commonly employed in numerous scientific investigations. However, many natural processes involve bond breaking and quantum forces. This complexity is compounded by the presence of multiple competing length and timescales. For example, accurately modeling the thermodynamics and dynamics of a chemical reaction requires accounting for the concerted movements of numerous solvent molecules and ions with their own fast or slow timescales. While widely used static Density Functional Theory (DFT) calculations at 0 temperature can be beneficial for such investigations, they do not account for dynamics, and lack precision in describing the molecular environments. They particularly fail at correct, rigorous treatments of finite-temperature fluctuations, and thus generalization to experimentally relevant conditions. In PNAS Benayad et al develop a scalable, generalizable approach for designing Neural Network Potentials (NNPs) that can handle chemical reactivity in solvated systems with quantum accuracy at classical costs. Specifically, they study phosphoester bond formation and rupture, which is fundamentally relevant to the Phosphorus-Oxygen bond formation central to life, and especially for the RNA world hypothesis. The framework developed here has the potential to generalize to different chemical reactions of energy and biological relevance.

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From Latent Dynamics to Meaningful Representations

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density — a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. Here, we show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.

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Enhanced Sampling of Crystal Nucleation with Graph Representation Learnt Variables

In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. Our approach uses simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine from their molten states. Our graph latent variables when biased in well-tempered metadynamics consistently show transitions between states and achieve accurate free energy calculations in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our graph neural net variables for improved sampling. Furthermore, the protocol shown here should be applicable for other systems and with other sampling methods.

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Is the Local Ion Density Sufficient to Drive NaCl Nucleation from the Melt and Aqueous Solution?

Even though nucleation is ubiquitous in different science and engineering problems, investigating nucleation is extremely difficult due to the complicated ranges of time and length scales involved. In this work, we simulate NaCl nucleation in both molten and aqueous environments using enhanced sampling of all-atom molecular dynamics with deep-learning-based estimation of reaction coordinates. By incorporating various structural order parameters and learning the reaction coordinate as a function thereof, we achieve significantly improved sampling relative to traditional ad hoc descriptions of what drives nucleation, particularly in an aqueous medium. Our results reveal a one-step nucleation mechanism in both environments, with reaction coordinate analysis highlighting the importance of local ion density in distinguishing solid and liquid states. However, although fluctuations in the local ion density are necessary to drive nucleation, they are not sufficient. Our analysis shows that near the transition states, descriptors such as enthalpy and local structure become crucial. Furthermore, our protocol proposed here enables robust nucleation analysis and phase sampling and could offer insights into nucleation mechanisms for generic small molecules in different environments.

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Thermodynamically Optimized Machine-Learned Reaction Coordinates for Hydrophobic Ligand Dissociation

Ligand unbinding is mediated by its free energy change, which has intertwined contributions from both energy and entropy. It is important, but not easy, to quantify their individual contributions to the free energy profile. We model hydrophobic ligand unbinding for two systems, a methane particle and a C 60 fullerene, both unbinding from hydrophobic pockets in all-atom water. Using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe the hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as the ligand and pocket sizes change. In both cases, we observe that the free-energy barrier to unbinding is dominated by entropy considerations. Furthermore, the process of methane unbinding is driven by methane solvation, while fullerene unbinding is driven first by pocket wetting and then fullerene wetting. For both solutes, the direct importance of the distance from the binding pocket to the learned reaction coordinate is present, but low. Furthermore, our framework and subsequent feature important analysis thus give useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean.

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Quantifying the Relevance of Long-Range Forces for Crystal Nucleation in Water

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture, elucidating the roles of different interactions in nucleation processes. In this study, we make use of three complementary techniques to disentangle the role played by short- and long-range interactions in solvent-mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Second, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Third, the deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from the LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state under ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from the combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

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Recent advances in describing and driving crystal nucleation using machine learning and artificial intelligence

With the advent of faster computer processors and especially graphics processing units (GPUs) over the last few decades, the use of data-intensive machine learning (ML) and artificial intelligence (AI) has increased greatly, and the study of crystal nucleation has been one of the beneficiaries. In this study, we outline how ML and AI have been applied to address four outstanding difficulties of crystal nucleation: how to discover better reaction coordinates (RCs) for describing accurately non-classical nucleation situations; the development of more accurate force fields for describing the nucleation of multiple polymorphs or phases for a single system; more robust identification methods for determining crystal phases and structures; and as a method to yield improved course-grained models for studying nucleation.

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Driving and characterizing nucleation of urea and glycine polymorphs in water

Crystal nucleation is relevant across the domains of fundamental and applied sciences. However, in many cases, its mechanism remains unclear due to a lack of temporal or spatial resolution. To gain insights into the molecular details of nucleation, some form of molecular dynamics simulations is typically performed; these simulations, in turn, are limited by their ability to run long enough to sample the nucleation event thoroughly. To overcome the timescale limits in typical molecular dynamics simulations in a manner free of prior human bias, here, we employ the machine learning-augmented molecular dynamics framework “reweighted autoencoded variational Bayes for enhanced sampling (RAVE).” We study two molecular systems—urea and glycine—in explicit all-atom water, due to their enrichment in polymorphic structures and common utility in commercial applications. From our simulations, we observe multiple back-and-forth nucleation events of different polymorphs from homogeneous solution; from these trajectories, we calculate the relative ranking of finite-sized polymorph crystals embedded in solution, in terms of the free-energy difference between the finite-sized crystal polymorph and the original solution state. We further observe that the obtained reaction coordinates and transitions are highly nonclassical.

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Path sampling of recurrent neural networks by incorporating known physics

Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections.

59 BASIC BIOLOGICAL SCIENCES↗

Artificial intelligence in computational materials science

In this themed collection we aim to broadly review some of the critical, recent progress in the application of AI/ML to various aspects of computational materials science and materials science more broadly. In this collection spread across two issues, we have assembled a collection of articles from leaders in the broad domain of applying AI/ML, which we collectively refer to as ML, in computational materials science. Together these articles curate the critical, recent progress in the application of ML to various aspects of materials science. Furthermore, these include ML approaches for understanding and driving electron microscopy, designing energy materials and the discovery of principles and materials relevant to the design of materials for the future, studying crystal nucleation and growth, the use of ML to describe force fields governing material and molecular behavior, and other topics.

36 MATERIALS SCIENCE↗

Quantifying Energetic and Entropic Pathways in Molecular Systems

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Lastly, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

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Influence of Long-Range Forces on the Transition States and Dynamics of NaCl Ion-Pair Dissociation in Water

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long-range Coulomb interactions and for a well-chosen reference system with short-range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool “State predictive information bottleneck” (SPIB), we show that the system with short-range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long-range interactions can be largely neglected for these processes because long-range forces from the direct interionic Coulomb interactions are almost completely canceled (>90%) by those from solvent interactions over the length scale where the transition takes place. Thus, for this important monovalent ion-pair system, short-range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short-range models for the dissociation event. Here, we believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long-range contributions may be more important.

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Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the “spectral gap optimization of order parameters (SGOOP)” approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. Here, we believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

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State predictive information bottleneck

We report the ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics simulations is heavily dependent on the knowledge of a low-dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states, and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work we propose a deep learning based state predictive information bottleneck approach to learn the RC from high-dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is connected to the committor in chemical physics and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time delay or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations.

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