Langevin Dynamics - Science topic

We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system–bath coupling is sufficiently strong, the Matsubara...

Mirror descent, introduced by Nemirovski and Yudin in the 1970s, is a primal-dual convex optimization method that can be tailored to the geometry of the optimization problem at hand through the choice of a strongly convex potential function. It arises as a basic primitive in a variety of applications, including large-scale optimization, machine lea...

We study how the typical gradient and typical height of a random surface are modified by the addition of quenched disorder in the form of a random independent external field. The results provide quantitative estimates, sharp up to multiplicative constants, in the following cases. It is shown that for real-valued random-field random surfaces of the...

The Born-Oppenheimer (BO) approximation has shaped our understanding on molecular dynamics microscopically in many physical and chemical systems. However, there are many cases that we must go beyond the BO approximation, particularly when strong light-matter interactions are considered. Floquet theory offers a powerful tool to treat time-periodic q...

In a viscoelastic environment, the diffusion of a particle becomes non-Markovian due to the memory effect. An open question is to quantitatively explain how self-propulsion particles with directional memory diffuse in such a medium. Based on simulations and analytic theory, we address this issue with active viscoelastic systems where an active part...

Stochastic Gradient Algorithms (SGAs) are ubiquitous in computational statistics, machine learning and optimisation. Recent years have brought an influx of interest in SGAs, and the non-asymptotic analysis of their bias is by now well-developed. However, relatively little is known about the optimal choice of the random approximation (e.g mini-batch...

A recent stochastic pursuit model describes a pack of chasers (hounds) that actively move toward a target (hare) that undergoes pure Brownian diffusion (Bernardi and Lindner, Phys. Rev. Lett. 2022). Here, this model is extended by introducing a deterministic ``escape term", which depends on the hounds' positions. In other words, the hare can ``see"...

We derive a quantum Langevin equation for a quantum spin in the presence of a magnetic field and coupled to a bath. We have considered two models for the bath: an Ohmic bath model and a non-Markovian Drude bath model with finite memory. The effect of finite memory on the dynamics of the quantum spin is studied in detail. In particular, we have stud...

A common problem that affects simulations of complex systems within the computational physics and chemistry communities is the so-called sampling problem or rare event problem where proper sampling of energy landscapes is impeded by the presences of high kinetic barriers that hinder transitions between metastable states on typical simulation time s...

We adopt an information-theoretic framework to analyze the generalization behavior of the class of iterative, noisy learning algorithms. This class is particularly suitable for study under information-theoretic metrics as the algorithms are inherently randomized, and it includes commonly used algorithms such as Stochastic Gradient Langevin Dynamics...

Memory effects are ubiquitous in a wide variety of complex physical phenomena, ranging from glassy dynamics and metamaterials to climate models. The Generalised Langevin Equation (GLE) provides a rigorous way to describe memory effects via the so-called memory kernel in an integro-differential equation. However, the memory kernel is often unknown,...

The nonequilibrium dynamics of light in a coherently driven nonlinear cavity resembles the equilibrium dynamics of a Brownian particle in a scalar potential. This resemblance has been known for decades, but the correspondence between the two systems has never been properly assessed. Here we demonstrate that this correspondence can be exact, be appr...

Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling based on greedy variance reduction and stochastic gradient Langevin dynamics (SGLD). The image priors involved c...

We prove that the Yang-Mills (YM) measure for the trivial principal bundle over the two-dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge-fixing, and Bourgain's method for invariant measures. Seve...

In this paper, we propose energy-based sample adaptation at test time for domain generalization. Where previous works adapt their models to target domains, we adapt the unseen target samples to source-trained models. To this end, we design a discriminative energy-based model, which is trained on source domains to jointly model the conditional distr...

Diffusion models have recently emerged as a powerful framework for generative modeling. They consist of a forward process that perturbs input data with Gaussian white noise and a reverse process that learns a score function to generate samples by denoising. Despite their tremendous success, they are mostly formulated on finite-dimensional spaces, e...

Score-based generative models (SGMs) have recently emerged as a promising class of generative models. However, a fundamental limitation is that their sampling process is slow due to a need for many (\eg, $2000$) iterations of sequential computations. An intuitive acceleration method is to reduce the sampling iterations which however causes severe p...

In this study the time evolution of energy and particles densities in burning plasma for D3He fuel in fusion reactors in the presence of thermal noise are investigated. The fusion reaction takes places in plasma of deuterium and helium3 heated to millions of degrees. It is expected that at this temperature, the thermal noise could have a significan...

Early detection of the COVID-19 virus is an important task for controlling the spread of the pandemic. Imaging techniques such as chest X-ray are relatively inexpensive and accessible, but its interpretation requires expert knowledge to evaluate the disease severity. Several approaches for automatic COVID-19 detection using deep learning techniques...

In this paper we announce the public release of a massively-parallel, GPU-accelerated software, which is the first to combine both coarse-grained molecular dynamics and field-theoretical simulations in one simulation package. MATILDA.FT (Mesoscale, Accelerated, Theoretically-Informed, Langevin, Dissipative particle dynamics, and Field Theory) was d...

Thermodynamics serves as a universal means for studying physical systems from an energy perspective. In recent years, with the establishment of the field of stochastic and quantum thermodynamics, the ideas of thermodynamics have been generalized to small fluctuating systems. Independently developed in mathematics and statistics, the optimal transpo...

We experimentally and theoretically investigate the dynamics and work fluctuations of an optically trapped micro-particle in a viscoelastic medium driven by an external Ornstein-Uhlenbeck (OU) noise. Compared to a viscous medium of the same zero-shear viscosity, we find a significant increase ($\sim 50 \%$) in the mean transferred power from the ex...

The energy landscape theory has widely been applied to study the stochastic dynamics of biological systems. Different methods have been developed to quantify the energy landscape for gene networks, e.g., using Gaussian approximation (GA) approach to calculate the landscape by solving the diffusion equation approximately from the first two moments....

This paper introduces a new neural network based prior for real valued functions. Each weight and bias of the neural network has an independent Gaussian prior, with the key novelty that the variances decrease in the width of the network in such a way that the resulting function is well defined in the limit of an infinite width network. We show that...

We proposed a new technique to accelerate sampling methods for solving difficult optimization problems. Our method investigates the intrinsic connection between posterior distribution sampling and optimization with Langevin dynamics, and then we propose an interacting particle scheme that approximates a Reweighted Interacting Langevin Diffusion sys...

The formation of biomolecular condensates by phase separation can be mimicked using fully synthetic, phase-separating DNA-nanomotifs, enabling remarkable control and performance increase in several functional nanomaterials. Stem cells exhibit prominent clusters of macromolecules controlling and executing transcription of genes into RNA, which also...

We present a new concept for the separation of DNA molecules by contour length that combines a nanofluidic ratchet, nanopore translocation, and pulsed fields. Using Langevin dynamics simulations, we show that it is possible to design pulsed field sequences to ratchet captured semiflexible molecules in such a way that only short chains successfully...

Instead of acquiring the previous aberrations of an optical wavefront with a sensor, wavefront sensor-less (WFSless) adaptive optics (AO) systems compensate for wavefront distortion by optimizing the performance metric directly. The stochastic parallel gradient descent (SPGD) algorithm is pervasively adopted to achieve performance metric optimizati...

In this paper, we are concerned with a non-asymptotic analysis of sampling algorithms used in nonconvex optimization. In particular, we obtain non-asymptotic estimates in Wasserstein-1 and Wasserstein-2 distances for a popular class of algorithms called Stochastic Gradient Langevin Dynamics (SGLD). In addition, the aforementioned Wasserstein-2 conv...

High-temperature properties of ceria surfaces are important for many applications. Here, we report the temperature dependencies of surface energy for (111) and (110) CeO2 obtained in the framework of the extended two-stage up-sampled thermodynamic integration using Langevin dynamics. The method was used together with machine-learning potentials cal...

The dynamics of a star-shaped polymer translocation pulled by a single arm through a nanochannel is investigated using three-dimensional Langevin dynamics simulations. The pulling force is applied on the terminal monomer of the leading arm in order to mimic the motion of chains subject to a combination of magnetic and optical tweezers in real exper...

Isoflux tension propagation (IFTP) theory and Langevin dynamics (LD) simulations are employed to study the dynamics of channel-driven polymer translocation in which a polymer translocates into a narrow channel and the monomers in the channel experience a driving force fc. In the high driving force limit, regardless of the channel width, IFTP theory...

Application of the replica exchange (i.e., parallel tempering) technique to Langevin Monte Carlo algorithms, especially stochastic gradient Langevin dynamics (SGLD), has scored great success in non-convex learning problems, but one potential limitation is the computational cost caused by running multiple chains. Upon observing that a large variance...

A two-stage model is developed to explain the phenomena of chain expansion, released from a confining cavity. In the first stage, the chain is assumed to expand as a sphere, while in the second stage it expands like a coil. The kinetic equations for the variation of chain size are derived in the two stages by balancing the rate of the free energy c...

We investigate collective properties of a large system of soft self-propelled inertial disks with active Langevin dynamics simulation in two dimensions. Rotational inertia of the disks is found to favor motility induced phase separation (MIPS), due to increased effective persistence of the disks. The MIPS phase diagram in the parameter space of rot...

The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that c...

We develop a new stochastic analysis approach to the lattice Yang–Mills model at strong coupling in any dimension \(d>1\), with t’ Hooft scaling \(\beta N\) for the inverse coupling strength. We study their Langevin dynamics, ergodicity, functional inequalities, large N limits, and mass gap. Assuming \(|\beta | < \frac{N-2}{32(d-1)N}\) for the stru...

Ensemble methods have become ubiquitous for the solution of Bayesian inference problems. State-of-the-art Langevin samplers such as the Ensemble Kalman Sampler (EKS), Affine Invariant Langevin Dynamics (ALDI) or its extension using weighted covariance estimates rely on successive evaluations of the forward model or its gradient. A main drawback of...

In this paper, we propose a cost-reduced method for finite-temperature molecular dynamics on a near-term quantum computer, Quantum Car-Parrinello molecular dynamics (QCPMD). One of the most promising applications of near-term quantum computers is quantum chemistry. It has been expected that simulations of molecules via molecular dynamics can be als...

We numerically investigate an adaptive version of the parareal algorithm in the context of molecular dynamics. This adaptive variant has been originally introduced in [F. Legoll, T. Lelievre and U. Sharma, SISC 2022]. We focus here on test cases of physical interest where the dynamics of the system is modelled by the Langevin equation and is simula...

Large language models can perform new tasks in a zero-shot fashion, given natural language prompts that specify the desired behavior. Such prompts are typically hand engineered, but can also be learned with gradient-based methods from labeled data. However, it is underexplored what factors make the prompts effective, especially when the prompts are...

Large crossed mixed effects models with imbalanced structures and missing data pose major computational challenges for standard Bayesian posterior sampling algorithms, as the computational complexity is usually superlinear in the number of observations. We propose two efficient subset-based stochastic gradient MCMC algorithms for such crossed mixed...

This paper proposes an iterative score-based generative model for solving the automatic colorization problem. Although unsupervised learning methods have shown the capability to generate plausible color, inadequate exploration of detailed information and data dimensions still limit the performance of the colorization model. Considering that the num...

The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate t...

Light is a complex-valued field. The intensity and phase of the field are affected by imaged objects. However, imaging sensors measure only real-valued non-negative intensities. This results in a nonlinear relation between the measurements and the unknown imaged objects. Moreover, the sensor readouts are corrupted by Poissonian-distributed photon n...

We study the uniform-in-time propagation of chaos for mean field Langevin dynamics with convex mean field potenital. Convergences in both Wasserstein-$2$ distance and relative entropy are established. We do not require the mean field potenital functional to bear either small mean field interaction or displacement convexity, which are common constra...

Protein structure prediction is a fundamental problem in computational molecular biology. Classical algorithms such as ab-initio or threading as well as many learning methods have been proposed to solve this challenging problem. However, most reinforcement learning methods tend to model the state-action pairs as discrete objects. In this paper, we...

Diffusion of small particles is omnipresent in a plentiful number of processes occurring in Nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow down our survey for the case of the diffusion coefficient for a Brown...

In this work we explore a new framework for approximate Bayesian inference in large datasets based on stochastic control. We advocate stochastic control as a finite time and low variance alternative to popular steady-state methods such as stochastic gradient Langevin dynamics. Furthermore, we discuss and adapt the existing theoretical guarantees of...

The work is devoted to the theoretical and numerical analysis of a two-component superparamagnetic system. Namely, of a rigid superparamagnetic cluster embedded in a superparamagnetic medium and subjected to a uniform magnetic field. Both cluster and the medium contain single-domain nanoparticles of the same diameter and magnetic moment. But the co...

Equilibrium properties in statistical physics are obtained by computing averages with respect to Boltzmann-Gibbs measures, sampled in practice using ergodic dynamics such as the Langevin dynamics. Some quantities however cannot be computed by simply sampling the Boltzmann-Gibbs measure, in particular transport coefficients, which relate the current...

Fluctuation theorems based on time-reversal have provided remarkable insight into the non-equilibrium statistics of thermodynamic quantities like heat, work, and entropy production. These types of laws impose constraints on the distributions of certain trajectory functionals that reflect underlying dynamical symmetries. In this work, we introduce a...

We present a practical asynchronous data fusion model for networked agents to perform distributed Bayesian learning without sharing raw data. Our algorithm uses a gossip-based approach where pairs of randomly selected agents employ unadjusted Langevin dynamics for parameter sampling. We also introduce an event-triggered mechanism to further reduce...

We consider the dynamics of a translocation process of a flexible linear polymer through a nanopore into an environment of active rods in the {\it trans} side. Using Langevin dynamics simulations we find that the rods facilitate translocation to the {\it trans} side even when there are initially more monomers on the {\it cis} than on the {\it trans...

Translocation dynamics of an active semi-flexible polymer through a nano-pore into a rigid two dimensional circular cavity, and the polymer packing dynamics have been studied by using Langevin dynamics (LD) simulations. The results show that the force exponent $\beta$, for regime of small cavity radius, i.e. $R \ll R_{\textrm{g}}$, where $R_{\textr...

We propose an approach for learning accurately the dynamics of slow collective variables from atomistic data obtained from ab-initio quantum mechanical theory, using generalized Langevin equations (GLE). The force fields, memory kernel, and noise generator are constructed within the Mori-Zwanzig formalism under the constraint imposed by the fluctua...

Bayesian methods of sampling from a posterior distribution are becoming increasingly popular due to their ability to precisely display the uncertainty of a model fit. Classical methods based on iterative random sampling and posterior evaluation such as Metropolis-Hastings are known to have desirable long run mixing properties, however are slow to c...

Combined effect of random forces of different origins and electrostatic confinement on the dynamics of a charged Brownian particle in a plasma is investigated. Analytical equations for the effective kinetic temperature, mean square displacement (MSD), mass transfer, and velocity autocorrelation functions (VAF) of a free and trapped microparticle un...

In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs), including additive, diagonal and scalar noise types. The central idea is to view the splitting method as a replacement of the driving signal of an SDE, namely Brownian m...

This paper proposes a replica exchange preconditioned Langevin diffusion discretized by the Crank-Nicolson scheme (repCNLD) to handle high-dimensional and multi-modal distribution problems. Sampling from high-dimensional and multi-modal distributions is a challenging question. The performance of many standard MCMC chains deteriorates as the dimensi...

Stochastic gradient MCMC (SGMCMC) offers a scalable alternative to traditional MCMC, by constructing an unbiased estimate of the gradient of the log-posterior with a small, uniformly-weighted subsample of the data. While efficient to compute, the resulting gradient estimator may exhibit a high variance and impact sampler performance. The problem of...

In recent years, several artificial molecular motors driven and controlled by electric currents have been proposed. Similar to Brownian machines, these systems work by turning random inelastic tunneling events into a directional rotation of the molecule. Despite their importance as the ultimate component of future molecular machines, their modeling...

We introduce a new Langevin dynamics based algorithm, called e-TH$\varepsilon$O POULA, to solve optimization problems with discontinuous stochastic gradients which naturally appear in real-world applications such as quantile estimation, vector quantization, CVaR minimization, and regularized optimization problems involving ReLU neural networks. We...

This paper proposes a methodology to estimate uncertainty in automated vehicle (AV) dynamics in real time via Bayesian inference. Based on the estimated uncertainty, the method aims to continuously monitor the car-following (CF) performance of the AV to support strategic actions to maintain a desired performance. Our methodology consists of three s...

We have studied the persistence probability $p(t)$ of an active Brownian particle with shape asymmetry in two dimensions. The persistence probability is defined as the the probability of a stochastic variable that has not changed it's sign in the fixed given time interval. We have investigated two cases- diffusion of a free active particle and that...

Bayesian Federated Learning (FL) offers a principled framework to account for the uncertainty caused by limitations in the data available at the nodes implementing collaborative training. In Bayesian FL, nodes exchange information about local posterior distributions over the model parameters space. This paper focuses on Bayesian FL implemented in a...