arXiv subjects

Aaron R. Dinner

Publications and source records attributed to Aaron R. Dinner.

At least 19 recordsLinked to original sources

arXiv2026

Nuclear Quantum Effects as a Denoising Problem

Nuclear quantum effects are rigorously captured by imaginary-time path integrals, which map the quantum Boltzmann distribution onto a ring polymer of classical replicas. Yet the nuclear masses, the coupling to the environment, and the boundary conditions of the path remain hard-wired in the simulation or the trained model, even though this quantum context enters the path measure only through a quadratic action known in closed form. Here we show that a denoiser trained on classical Boltzmann statistics alone, composed at sampling time with an analytic Gaussian component carrying the entire quantum context, yields the quantum Boltzmann distribution of the nuclei. Such a composition exists and is exact whenever the training noise does not exceed the intrinsic quantum uncertainty of the target ensemble, and it is invariant across all quantum contexts admitted by this bound. We show exact transfer across temperature, isotopic mass, dissipation strength, and the boundary conditions of the path in theory and in numerical experiments, without retraining. The last yields the end-to-end displacement and momentum distributions of a tagged nucleus from open imaginary-time paths. The same invariance extends in principle to the permuted boundary conditions of bosonic exchange, with the identical denoiser. In this view, the noise of generative modeling and the quantum fluctuations of the nuclei are two faces of the same quadratic structure.

physics.chem-ph↗

arXiv2026

Composing diffusion priors with explicit physical context via generative Gibbs sampling

Pretrained diffusion models provide powerful learned priors, but in scientific sampling the target distribution often depends on physical context that is not fully represented by one generative model. We introduce Generative Gibbs for Physics-Aware Sampling (GG-PA), a training-free framework that formulates the composition of learned partial priors and explicit physical context as inference over a joint target distribution in an augmented state space. We derive a Gibbs sampler for this joint target, show that it is asymptotically exact as the diffusion time approaches zero, and prove that in settings with quadratic interactions it remains exact at finite diffusion times. We further introduce replica exchange over diffusion time to accelerate mixing. Experiments on a double-well system, a $\phi^4$ lattice model, and atomistic peptide systems show that GG-PA recovers context-induced distribution shifts and emergent collective behavior in interacting systems using partial priors without retraining. These results demonstrate GG-PA as a practical approach for combining pretrained generative priors with explicit physical context.

cs.LG↗

arXiv2026

Adaptive tensor train metadynamics for high-dimensional free energy exploration

A key challenge for molecular dynamics simulations is efficient exploration of free energy landscapes over relevant collective variables (CV). Common methods for enhancing sampling become prohibitively inefficient beyond only a few CVs; in the case of the widely-used metadynamics method, the computational cost of evaluating and storing the bias potential grows exponentially with the number of dimensions. Here, we introduce TT-Metadynamics, in which the accumulated sum of Gaussian functions in the original metadynamics method is periodically compressed into a low-rank tensor train (TT) representation. The TT enables efficient memory use and prevents the computational cost of evaluating the bias potential from increasing with simulation time. We present a "sketching" algorithm that allows us to construct the TT with linear scaling in the number of CVs. Applied to benchmark systems with up to 14 CVs, the accuracy of TT-Metadynamics matches or exceeds that of standard metadynamics in long simulations, particularly in systems with high barriers. These results establish TT-Metadynamics as a scalable and effective method for computing free energies that are functions of several CVs.

physics.chem-ph↗

arXiv2026

Quantum statistics from classical simulations via generative Gibbs sampling

Accurate simulation of nuclear quantum effects is essential for molecular modeling but expensive using path integral molecular dynamics (PIMD). We present GG-PI, a ring-polymer-based framework that combines generative modeling of the single-bead conditional density with Gibbs sampling to recover quantum statistics from classical simulation data. GG-PI uses inexpensive standard classical simulations or existing data for training and allows transfer across temperatures without retraining. On standard test systems, GG-PI significantly reduces wall clock time compared to PIMD. Our approach extends easily to a wide range of problems with similar Markov structure.

physics.chem-ph↗

arXiv2026

In-context learning emerges in chemical reaction networks without attention

We investigate whether chemical processes can perform in-context learning (ICL), a mode of computation typically associated with transformer architectures. ICL allows a system to infer task-specific rules from a sequence of examples without relying solely on fixed parameters. Traditional ICL relies on a pairwise attention mechanism which is not obviously implementable in chemical systems. However, we show theoretically and numerically that chemical processes can achieve ICL through a mechanism we call subspace projection, in which the entire input vector is mapped onto comparison subspaces, with the dominant projection determining the computational output. We illustrate this mechanism analytically in small chemical systems and show numerically that performance is robust to input encoding and dynamical choices, with the number of tunable degrees of freedom in the input encoding as a key limitation. Our results provide a blueprint for realizing ICL in chemical or other physical media and suggest new directions for designing adaptive synthetic chemical systems and understanding possible biological computation in cells.

cond-mat.dis-nn↗

arXiv2025

Hierarchical geometric deep learning enables scalable analysis of molecular dynamics

Molecular dynamics simulations can generate atomically detailed trajectories of complex systems, but analyzing these dynamics can be challenging when systems lack well-established quantitative descriptors (features). Graph neural networks (GNNs) in which messages are passed between nodes that represent atoms that are spatial neighbors promise to obviate manual feature engineering, but the use of GNNs with biomolecular systems of more than a few hundred residues has been limited in the context of analyzing dynamics by both difficulties in capturing the details of long-range interactions with message passing and the memory and runtime requirements associated with large graphs. Here, we show how local information can be aggregated to reduce memory and runtime requirements without sacrificing atomic detail. We demonstrate that this approach opens the door to analyzing simulations of protein-nucleic acid complexes with thousands of residues on single GPUs within minutes. For systems with hundreds of residues, for which there are sufficient data to make quantitative comparisons, we show that the approach improves performance and interpretability.

cs.LG↗

arXiv2025

An exact multiple-time-step variational formulation for the committor and the transition rate

For a transition between two stable states, the committor is the probability that the dynamics leads to one stable state before the other. It can be estimated from trajectory data by minimizing an expression for the transition rate that depends on a lag time. We show that an existing such expression is minimized by the exact committor only when the lag time is a single time step, resulting in a biased estimate in practical applications. We introduce an alternative expression that is minimized by the exact committor at any lag time. The key idea is that, when trajectories enter the stable states, the times that they enter (stopping times) must be used for estimating the committor and transition rate instead of the lag time. Numerical tests on benchmark systems demonstrate that our committor and transition rate estimates are much less sensitive to the choice of lag time. We show how further accuracy for the transition rate can be achieved by combining results from two lag times. We also relate the transition rate expression to a variational approach for kinetic statistics based on the mean-squared residual and discuss further numerical considerations with the aid of a decomposition of the error into dynamic modes.

cond-mat.stat-mech↗

arXiv2025

Local imperfect feedback control in non-equilibrium biophysical systems enabled by thermodynamic constraints

How biological networks achieve robust control despite relying on imperfect, local information remains an important open question. Here, we identify thermodynamic constraints that can curtail non-equilibrium steady-state responses so severely that even crude, local feedback rules can achieve globally stable control without requiring precise network design or global information. Specifically, using Markov jump processes as a general framework for biophysical dynamics, we derive general non-equilibrium response constraints showing that for many classes of rate perturbations, steady-state responses have fixed signs across all driving strengths, so that near-equilibrium responses predict far-from-equilibrium behavior regardless of system complexity. These constraints clarify several biological phenomena: monotonicity is thermodynamically guaranteed whenever a perturbation acts on a single transition rate, and non-monotonic responses, as observed for example in transcription factor regulation, arise only when an input simultaneously modulates multiple rates. Even in this case, we identify a graph-theoretic concept termed ``coherence'' that allows for a restoration of monotonicity. We show how coherence naturally and generally emerges in classic biophysical models of adaptation, including E. coli chemotaxis, and transcription factor regulation when biological constraints on network parameterization are included. We next show that, within a control-theoretic framework, these constraints guarantee that simple linear feedback on small subsets of kinetic rates achieves globally stable tracking and adaptation without coordinated manipulation of many variables. For systems with one regulator, local stability implies global stability for arbitrary network topologies without fine tuning, revealing that non-equilibrium thermodynamics fundamentally constrains biochemical network responses.

cond-mat.stat-mech↗

arXiv2025

Mitigating mode collapse in normalizing flows by annealing with an adaptive schedule: Application to parameter estimation

Normalizing flows (NFs) provide uncorrelated samples from complex distributions, making them an appealing tool for parameter estimation. However, the practical utility of NFs remains limited by their tendency to collapse to a single mode of a multimodal distribution. In this study, we show that annealing with an adaptive schedule based on the effective sample size (ESS) can mitigate mode collapse. We demonstrate that our approach can converge the marginal likelihood for a biochemical oscillator model fit to time-series data in ten-fold less computation time than a widely used ensemble Markov chain Monte Carlo (MCMC) method. We show that the ESS can also be used to reduce variance by pruning the samples. We expect these developments to be of general use for sampling with NFs and discuss potential opportunities for further improvements.

cs.LG↗

arXiv2025

Renormalized mechanics and stochastic thermodynamics of growing vesicles

Uncovering the rules governing the nonequilibrium dynamics of the membranes that define biological cells is of central importance to understanding the physics of living systems. We theoretically and computationally investigate the behavior of flexible quasispherical vesicles that exchange membrane constituents, internal volume, and heat with an external reservoir. The excess chemical potential and osmotic pressure difference imposed by the reservoir act as generalized thermodynamic driving forces that modulate vesicle morphology. We show that the renormalization of membrane mechanical properties by nonequilibrium driving gives rise to a morphological transition between a weakly driven regime, in which growing vesicles remain quasispherical, and a strongly driven regime, in which vesicles accommodate rapid membrane uptake by developing surface wrinkles. Additionally, we propose a minimal vesicle growth-shape law, derived using insights from stochastic thermodynamics, that robustly describes vesicle growth dynamics even in strongly driven, far-from-equilibrium regimes.

cond-mat.soft↗

arXiv2025

Characterizing nonlinear dynamics by contrastive cartography

The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an unknown number of attractors, and stochasticity. Characterization of these often-complicated behaviors remains challenging. Making an analogy to bifurcation analysis, which specifies that useful dynamical features are often invariant to coordinate transforms, we leverage contrastive learning to devise a generic tool to discover dynamical classes from stochastic trajectory data. By providing a model-free trajectory analysis tool, this method automatically recovers the dynamical phase diagram of known models and provides a "map" of dynamical behaviors for a large ensemble of dynamical systems. The method thus provides a way to characterize and compare dynamical trajectories without governing equations or prior knowledge of target behavior. We additionally show that the same strategy can be used to characterize the stochastic motion of bacteria, establishing that this approach can be used as a standalone analysis tool or as a component of a broader data-driven analysis framework for dynamical data.

nlin.CD↗

arXiv2024

Tailoring interactions between active nematic defects with reinforcement learning

Active nematics, formed from a liquid crystalline suspension of active force dipoles, are a paradigmatic active matter system whose study provides insights into how chemical driving produces the cellular mechanical forces essential for life. Recent advances in optogenetic control over molecular motors and cell-signaling pathways now allow experimenters to mimic the spatiotemporal regulation of activity necessary to drive biologically relevant active nematic flows in vivo. However, engineering effective activity protocols remains challenging due to the system's complex dynamics. Here, we explore a model-free approach for controlling active nematic fields using reinforcement learning. Specifically, we demonstrate how local activity fields can induce interactions between pairs of nematic defects, enabling them to follow designer dynamical laws such as those of overdamped springs with varying stiffnesses. Reinforcement learning bypasses the need for accurate parameterization and model representation of the nematic system, and could thus transfer straightforwardly to experimental implementation. Moreover, the sufficiency of our low-dimensional system observables and actions suggests that coarse projections of the active nematic field can be used for precise feedback control, making the biological implementation of such feedback loops plausible.

cond-mat.soft↗

arXiv2024

Using pretrained graph neural networks with token mixers as geometric featurizers for conformational dynamics

Identifying informative low-dimensional features that characterize dynamics in molecular simulations remains a challenge, often requiring extensive manual tuning and system-specific knowledge. Here, we introduce geom2vec, in which pretrained graph neural networks (GNNs) are used as universal geometric featurizers. By pretraining equivariant GNNs on a large dataset of molecular conformations with a self-supervised denoising objective, we obtain transferable structural representations that are useful for learning conformational dynamics without further fine-tuning. We show how the learned GNN representations can capture interpretable relationships between structural units (tokens) by combining them with expressive token mixers. Importantly, decoupling training the GNNs from training for downstream tasks enables analysis of larger molecular graphs (such as small proteins at all-atom resolution) with limited computational resources. In these ways, geom2vec eliminates the need for manual feature selection and increases the robustness of simulation analyses.

cs.LG↗

arXiv2024

Limits on the computational expressivity of non-equilibrium biophysical processes

Many biological decision-making processes can be viewed as performing a classification task over a set of inputs, using various chemical and physical processes as "biological hardware." In this context, it is important to understand the inherent limitations on the computational expressivity of classification functions instantiated in biophysical media. Here, we model biochemical networks as Markov jump processes and train them to perform classification tasks, allowing us to investigate their computational expressivity. We reveal several unanticipated limitations on the input-output functions of these systems, which we further show can be lifted using biochemical mechanisms like promiscuous binding. We analyze the flexibility and sharpness of decision boundaries as well as the classification capacity of these networks. Additionally, we identify distinctive signatures of networks trained for classification, including the emergence of correlated subsets of spanning trees and a creased "energy landscape" with multiple basins. Our findings have implications for understanding and designing physical computing systems in both biological and synthetic chemical settings.

cond-mat.dis-nn↗

arXiv2024

Sampling parameters of ordinary differential equations with Langevin dynamics that satisfy constraints

Fitting models to data to obtain distributions of consistent parameter values is important for uncertainty quantification, model comparison, and prediction. Standard Markov chain Monte Carlo (MCMC) approaches for fitting ordinary differential equations (ODEs) to time-series data involve proposing trial parameter sets, numerically integrating the ODEs forward in time, and accepting or rejecting the trial parameter sets. When the model dynamics depend nonlinearly on the parameters, as is generally the case, trial parameter sets are often rejected, and MCMC approaches become prohibitively computationally costly to converge. Here, we build on methods for numerical continuation and trajectory optimization to introduce an approach in which we use Langevin dynamics in the joint space of variables and parameters to sample models that satisfy constraints on the dynamics. We demonstrate the method by sampling Hopf bifurcations and limit cycles of a model of a biochemical oscillator in a Bayesian framework for parameter estimation, and we attain performance that matches or exceeds the performance of leading MCMC approaches that require numerically integrating the ODEs forward in time. We describe numerical experiments that provide insight into the speedup. The method is general and can be used in any framework for parameter estimation and model selection.

stat.CO↗

arXiv2024

BAD-NEUS: Rapidly converging trajectory stratification

An issue for molecular dynamics simulations is that events of interest often involve timescales that are much longer than the simulation time step, which is set by the fastest timescales of the model. Because of this timescale separation, direct simulation of many events is prohibitively computationally costly. This issue can be overcome by aggregating information from many relatively short simulations that sample segments of trajectories involving events of interest. This is the strategy of Markov state models (MSMs) and related approaches, but such methods suffer from approximation error because the variables defining the states generally do not capture the dynamics fully. By contrast, once converged, the weighted ensemble (WE) method aggregates information from trajectory segments so as to yield unbiased estimates of both thermodynamic and kinetic statistics. Unfortunately, errors decay no faster than unbiased simulation in WE as originally formulated and commonly deployed. Here we introduce a theoretical framework for describing WE that shows that introduction of an approximate stationary distribution on top of the stratification, as in nonequilibrium umbrella sampling (NEUS), accelerates convergence. Building on ideas from MSMs and related methods, we generalize the NEUS approach in such a way that the approximation error can be reduced systematically. We show that the improved algorithm can decrease simulation times required to achieve a desired precision by orders of magnitude.

cond-mat.stat-mech↗

arXiv2024

Learning to control non-equilibrium dynamics using local imperfect gradients

Standard approaches to controlling dynamical systems involve biologically implausible steps such as backpropagation of errors or intermediate model-based system representations. Recent advances in machine learning have shown that "imperfect" feedback of errors during training can yield test performance that is similar to using full backpropagated errors, provided that the two error signals are at least somewhat aligned. Inspired by such methods, we introduce an iterative, spatiotemporally local protocol to learn driving forces and control non-equilibrium dynamical systems using imperfect feedback signals. We present numerical experiments and theoretical justification for several examples. For systems in conservative force fields that are driven by external time-dependent protocols, our update rules resemble a dynamical version of contrastive divergence. We appeal to linear response theory to establish that our imperfect update rules are locally convergent for these conservative systems. Finally, we show that similar local update rules can also solve dynamical control problems for non-conservative systems, and we illustrate this in the non-trivial example of active nematics. Our updates allow learning spatiotemporal activity fields that pull topological defects along desired trajectories in the active nematic fluid. These imperfect feedback methods are information efficient and in principle biologically plausible, and they can help extend recent methods of decentralized training for physical materials into dynamical settings.

cond-mat.stat-mech↗

arXiv2023

Accurate estimates of dynamical statistics using memory

Many chemical reactions and molecular processes occur on timescales that are significantly longer than those accessible by direct simulation. One successful approach to estimating dynamical statistics for such processes is to use many short time series observations of the system to construct a Markov state model (MSM), which approximates the dynamics of the system as memoryless transitions between a set of discrete states. The dynamical Galerkin approximation (DGA) generalizes MSMs for the problem of calculating dynamical statistics, such as committors and mean first passage times, by replacing the set of discrete states with a projection onto a basis. Because the projected dynamics are generally not memoryless, the Markov approximation can result in significant systematic error. Inspired by quasi-Markov state models, which employ the generalized master equation to encode memory resulting from the projection, we reformulate DGA to account for memory and analyze its performance on two systems: a two-dimensional triple well and helix-to-helix transitions of the AIB$_9$ peptide. We demonstrate that our method is robust to the choice of basis and can decrease the time series length required to obtain accurate kinetics by an order of magnitude.

physics.comp-ph↗