arXiv subjects

Grant M. Rotskoff

Publications and source records attributed to Grant M. Rotskoff.

At least 37 records · Page 2Linked to original sources

arXiv2024

Universal energy-speed-accuracy trade-offs in driven nonequilibrium systems

Physical systems driven away from equilibrium by an external controller dissipate heat to the environment; the excess entropy production in the thermal reservoir can be interpreted as a "cost" to transform the system in a finite time. The connection between measure theoretic optimal transport and dissipative nonequilibrium dynamics provides a language for quantifying this cost and has resulted in a collection of "thermodynamic speed limits", which argue that the minimum dissipation of a transformation between two probability distributions is directly proportional to the rate of driving. Thermodynamic speed limits rely on the assumption that the target probability distribution is perfectly realized, which is almost never the case in experiments or numerical simulations. Here, we address the ubiquitous situation in which the external controller is imperfect. As a consequence, we obtain a lower bound for the dissipated work in generic nonequilibrium control problems that 1) is asymptotically tight and 2) matches the thermodynamic speed limit in the case of optimal driving. We illustrate these bounds on analytically solvable examples and also develop a strategy for optimizing minimally dissipative protocols based on optimal transport flow matching, a generative machine learning technique. This latter approach ensures the scalability of both the theoretical and computational framework we put forth. Crucially, we demonstrate that we can compute the terms in our bound numerically using efficient algorithms from the computational optimal transport literature and that the protocols that we learn saturate the bound.

cond-mat.stat-mech↗

arXiv2024

Scaling field-theoretic simulation for multi-component mixtures with neural operators

Multi-component polymer mixtures are ubiquitous in biological self-organization but are notoriously difficult to study computationally. Plagued by both slow single molecule relaxation times and slow equilibration within dense mixtures, molecular dynamics simulations are typically infeasible at the spatial scales required to study the stability of mesophase structure. Polymer field theories offer an attractive alternative, but analytical calculations are only tractable for mean-field theories and nearby perturbations, constraints that become especially problematic for fluctuation-induced effects such as coacervation. Here, we show that a recently developed technique for obtaining numerical solutions to partial differential equations based on operator learning, *neural operators*, lends itself to a highly scalable training strategy by parallelizing per-species operator maps. We illustrate the efficacy of our approach on six-component mixtures with randomly selected compositions and that it significantly outperforms the state-of-the-art pseudospectral integrators for field-theoretic simulations, especially as polymer lengths become long.

cond-mat.soft↗

arXiv2024

Coacervation drives morphological diversity of mRNA encapsulating nanoparticles

The spatial arrangement of components within an mRNA encapsulating nanoparticle has consequences for its thermal stability, which is a key parameter for therapeutic utility. The mesostructure of mRNA nanoparticles formed with cationic polymers have several distinct putative structures: here, we develop a field theoretic simulation model to compute the phase diagram for amphiphilic block copolymers that balance coacervation and hydrophobicity as driving forces for assembly. We predict several distinct morphologies for the mesostructure of these nanoparticles, depending on salt conditions and hydrophobicity. We compare our predictions with cryogenic-electron microscopy images of mRNA encapsulated by charge altering releasable transporters. In addition, we provide a GPU-accelerated, open-source codebase for general purpose field theoretic simulations, which we anticipate will be a useful tool for the community.

cond-mat.soft↗

arXiv2024

Accurate and efficient structure elucidation from routine one-dimensional NMR spectra using multitask machine learning

Rapid determination of molecular structures can greatly accelerate workflows across many chemical disciplines. However, elucidating structure using only one-dimensional (1D) NMR spectra, the most readily accessible data, remains an extremely challenging problem because of the combinatorial explosion of the number of possible molecules as the number of constituent atoms is increased. Here, we introduce a multitask machine learning framework that predicts the molecular structure (formula and connectivity) of an unknown compound solely based on its 1D 1H and/or 13C NMR spectra. First, we show how a transformer architecture can be constructed to efficiently solve the task, traditionally performed by chemists, of assembling large numbers of molecular fragments into molecular structures. Integrating this capability with a convolutional neural network (CNN), we build an end-to-end model for predicting structure from spectra that is fast and accurate. We demonstrate the effectiveness of this framework on molecules with up to 19 heavy (non-hydrogen) atoms, a size for which there are trillions of possible structures. Without relying on any prior chemical knowledge such as the molecular formula, we show that our approach predicts the exact molecule 69.6% of the time within the first 15 predictions, reducing the search space by up to 11 orders of magnitude.

physics.chem-ph↗

arXiv2024

Committor guided estimates of molecular transition rates

The probability that a configuration of a physical system reacts, or transitions from one metastable state to another, is quantified by the committor function. This function contains richly detailed mechanistic information about transition pathways, but a full parameterization of the committor requires building representing a high-dimensional function, a generically challenging task. Recent efforts to leverage neural networks as a means to solve high-dimensional partial differential equations, often called "physics-informed" machine learning, have brought the committor into computational reach. Here, we build on the semigroup approach to learning the committor and assess its utility for predicting dynamical quantities such as transition rates. We show that a careful reframing of the objective function and improved adaptive sampling strategies provide highly accurate representations of the committor. Furthermore, by directly applying the Hill relation, we show that these committors provide accurate transition rates for molecular system.

cond-mat.stat-mech↗

arXiv2024

Discrete generative diffusion models without stochastic differential equations: a tensor network approach

Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a ``score function'' that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such ``discrete diffusion models'' (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the $d=1$ constrained Fredkin chain and the $d=2$ Ising model.

cond-mat.stat-mech↗

arXiv2024

Computing Nonequilibrium Responses with Score-shifted Stochastic Differential Equations

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic dynamics. For nonequilibrium systems, perturbations cannot be interpreted simply by monitoring fluctuations in a conjugate observable -- additional dynamical information is needed. The theory of linear response around nonequilibrium steady states relies on path ensemble averaging, which makes this theory inapplicable to perturbations that affect the diffusion constant or temperature in a stochastic system. Here, we show that a separate, ``effective'' physical process can be used to describe the perturbed dynamics and that this dynamics in turn allows us to accurately calculate the response to a change in the diffusion. Interestingly, the effective dynamics contains an additional drift that is proportional to the ``score'' of the instantaneous probability density of the system -- this object has also been studied extensively in recent years in the context of denoising diffusion models in the machine learning literature. Exploiting recently developed algorithms for learning the score, we show that we can carry out nonequilibrium response calculations on systems for which the exact score cannot be obtained.

cond-mat.stat-mech↗

arXiv2024

Quantum Hardware-Enabled Molecular Dynamics via Transfer Learning

The ability to perform ab initio molecular dynamics simulations using potential energies calculated on quantum computers would allow virtually exact dynamics for chemical and biochemical systems, with substantial impacts on the fields of catalysis and biophysics. However, noisy hardware, the costs of computing gradients, and the number of qubits required to simulate large systems present major challenges to realizing the potential of dynamical simulations using quantum hardware. Here, we demonstrate that some of these issues can be mitigated by recent advances in machine learning. By combining transfer learning with techniques for building machine-learned potential energy surfaces, we propose a new path forward for molecular dynamics simulations on quantum hardware. We use transfer learning to reduce the number of energy evaluations that use quantum hardware by first training models on larger, less accurate classical datasets and then refining them on smaller, more accurate quantum datasets. We demonstrate this approach by training machine learning models to predict a molecule's potential energy using Behler-Parrinello neural networks. When successfully trained, the model enables energy gradient predictions necessary for dynamics simulations that cannot be readily obtained directly from quantum hardware. To reduce the quantum resources needed, the model is initially trained with data derived from low-cost techniques, such as Density Functional Theory, and subsequently refined with a smaller dataset obtained from the optimization of the Unitary Coupled Cluster ansatz. We show that this approach significantly reduces the size of the quantum training dataset while capturing the high accuracies needed for quantum chemistry simulations.

physics.chem-ph↗

arXiv2024

Microscopic origin of tunable assembly forces in chiral active environments

The fluctuations of a nonequilibrium bath enable dynamics inaccessible to any equilibrium system. Exploiting the driven dynamics of active matter in order to do useful work has become a topic of significant experimental and theoretical interest. Due to the unique modalities controlling self-assembly, the interplay between passive solutes and the particles in an active bath has been studied as a potential driving force to guide assembly of otherwise non-interacting objects. Here, we investigate and characterize the microscopic origins of the attractive and repulsive interactions between passive solutes in an active bath. We show that, while assembly does not occur dynamically for achiral active baths, chiral active particles can produce stable and robust assembly forces. We both explain the observed oscillatory force profile for active Brownian particles and demonstrate that chiral active motion leads to fluxes consistent with an odd diffusion tensor that, when appropriately tuned, produces long-ranged assembly forces.

cond-mat.soft↗

arXiv2024

Data-efficient generation of protein conformational ensembles with backbone-to-side chain transformers

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are not currently data sources with sufficient breadth to parameterize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here we introduce a modular strategy to generate conformations based on ``backmapping'' from a fixed protein backbone that 1) maintains conformational diversity of the side chains and 2) couples the side chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquistion and hence a crucial ingredient for scalable physical simulation with generative neural networks.

cond-mat.stat-mech↗

arXiv2023

Statistical Spatially Inhomogeneous Diffusion Inference

Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments. Assuming that the underlying dynamical process obeys a $d$-dimensional stochastic differential equation of the form $$\mathrm{d}\boldsymbol{x}_t=\boldsymbol{b}(\boldsymbol{x}_t)\mathrm{d} t+Σ(\boldsymbol{x}_t)\mathrm{d}\boldsymbol{w}_t,$$ we propose neural network-based estimators of both the drift $\boldsymbol{b}$ and the spatially-inhomogeneous diffusion tensor $D = ΣΣ^{T}$ and provide statistical convergence guarantees when $\boldsymbol{b}$ and $D$ are $s$-Hölder continuous. Notably, our bound aligns with the minimax optimal rate $N^{-\frac{2s}{2s+d}}$ for nonparametric function estimation even in the presence of correlation within observational data, which necessitates careful handling when establishing fast-rate generalization bounds. Our theoretical results are bolstered by numerical experiments demonstrating accurate inference of spatially-inhomogeneous diffusion tensors.

stat.ML↗

arXiv2023

Computing equilibrium free energies through a nonequilibrium quench

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium "quench" process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of $N$-independent harmonic springs, and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling.= We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach, but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

physics.chem-ph↗

arXiv2023

Adaptive nonequilibrium design of actin-based metamaterials: fundamental and practical limits of control

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials and their properties. In particular, controlling the conditions of self-assembly can modulate material properties, but there is no systematic understanding of either how to parameterize this control or how \emph{controllable} a given material can be. Here, we demonstrate that branched actin networks can be encoded with \textit{metamaterial} properties by dynamically controlling the applied force under which they grow, and that the protocols can be selected using multi-task reinforcement learning. These actin networks have tunable responses over a large dynamic range depending on the chosen external protocol, providing a pathway to encoding ``memory'' within these structures. Interestingly, we show that encoding memory requires dissipation and the rate of encoding is constrained by the flow of entropy -- both physical and information theoretical. Taken together, these results emphasize the utility and necessity of nonequilibrium control for designing self-assembled nanostructures.

cond-mat.stat-mech↗

arXiv2023

Remembering the work of Phillip L. Geissler: A coda to his scientific trajectory

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective, we celebrate his work at these frontiers.

cond-mat.stat-mech↗

arXiv2022

A unified, geometric framework for nonequilibrium protocol optimization

Controlling thermodynamic cycles to minimize the dissipated heat is a longstanding goal in thermodynamics, and more recently, a central challenge in stochastic thermodynamics for nanoscale systems. Here, we introduce a theoretical and computational framework for optimizing nonequilibrium control protocols that can transform a system between two distributions in a minimally dissipative fashion. These protocols optimally transport a system along paths through the space of probability distributions that minimize the dissipative cost of a transformation. Furthermore, we show that the thermodynamic metric -- determined via a linear response approach -- can be directly derived from the same objective function that is optimized in the optimal transport problem, thus providing a unified perspective on thermodynamic geometries. We investigate this unified geometric framework in two model systems and observe that our procedure for optimizing control protocols is robust beyond linear response.

cond-mat.stat-mech↗

arXiv2022

Ensuring thermodynamic consistency with invertible coarse-graining

Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the thermodynamic properties of a complex, condensed-phase system. The reduced complexity of the model typically leads to lower computational costs and more efficient sampling compared to atomistic models. Designing ``good'' coarse-grained models is an art. Generally, the mapping from fine-grained configurations to coarse-grained configurations itself is not optimized in any way; instead, the energy function associated with the mapped configurations is. In this work, we explore the consequences of optimizing the coarse-grained representation alongside its potential energy function. We use a graph machine learning framework to embed atomic configurations into a low dimensional space to produce efficient representations of the original molecular system. Because the representation we obtain is no longer directly interpretable as a real space representation of the atomic coordinates, we also introduce an inversion process and an associated thermodynamic consistency relation that allows us to rigorously sample fine-grained configurations conditioned on the coarse-grained sampling. We show that this technique is robust, recovering the first two moments of the distribution of several observables in proteins such as chignolin and alanine dipeptide.

cond-mat.stat-mech↗

arXiv2022

Physics-informed graph neural networks enhance scalability of variational nonequilibrium optimal control

When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a current or entropy production rate, has become a central problem in nonequilibrium statistical mechanics. Asymptotically, for a broad class of observables, the distribution of a given observable satisfies a large deviation principle when the dynamics is Markovian, meaning that fluctuations can be characterized in the long-time limit by computing a scaled cumulant generating function. Calculating this function is not tractable analytically (nor often numerically) for complex, interacting systems, so the development of robust numerical techniques to carry out this computation is needed to probe the properties of nonequilibrium materials. Here, we describe an algorithm that recasts this task as an optimal control problem that can be solved variationally. We solve for optimal control forces using neural network ansätze that are tailored to the physical systems to which the forces are applied. We demonstrate that this approach leads to transferable and accurate solutions in two systems featuring large numbers of interacting particles.

cond-mat.stat-mech↗

arXiv2022

A Dynamical Central Limit Theorem for Shallow Neural Networks

Recent theoretical works have characterized the dynamics of wide shallow neural networks trained via gradient descent in an asymptotic mean-field limit when the width tends towards infinity. At initialization, the random sampling of the parameters leads to deviations from the mean-field limit dictated by the classical Central Limit Theorem (CLT). However, since gradient descent induces correlations among the parameters, it is of interest to analyze how these fluctuations evolve. Here, we use a dynamical CLT to prove that the asymptotic fluctuations around the mean limit remain bounded in mean square throughout training. The upper bound is given by a Monte-Carlo resampling error, with a variance that that depends on the 2-norm of the underlying measure, which also controls the generalization error. This motivates the use of this 2-norm as a regularization term during training. Furthermore, if the mean-field dynamics converges to a measure that interpolates the training data, we prove that the asymptotic deviation eventually vanishes in the CLT scaling. We also complement these results with numerical experiments.

math.PR↗