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Results for “Overdamped Langevin dynamics”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Essential barrier height and a probabilistic approach in characterizing potential landscape

In this work we propose a probabilistic approach to investigate the shape of landscapes of multi-dimensional potential functions. Under a suitable coupling scheme, two copies of the overdamped Langevin dynamics associated with the potential function are coupled, and the coupling times are collected. Assuming a set of intuitive yet technically challenging conditions on the coupling scheme, it is shown that the tail distributions of the coupling times exhibit qualitatively different dependencies on the noise magnitude for single-well versus multi-well potential functions. More specifically, for convex single-well potentials, the negative tail exponent of the coupling time distribution is uniformly bounded away from zero by the convexity parameter and is independent of the noise magnitude. In contrast, for multi-well potentials, the negative tail exponent decreases exponentially as the noise vanishes, with the decay rate governed by the essential barrier height, a quantity introduced in this paper to characterize the non-convex nature of the potential function. Numerical investigations are conducted for a variety of examples, including the Rosenbrock function, interacting particle systems, and loss functions arising in artificial neural networks. These examples not only illustrate the theoretical results in various contexts but also provide crucial numerical validation of the conjectured assumptions, which are essential to the theoretical analysis yet lie beyond the reach of standard technical tools.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Nonlocal Effect of Percolated Particle Networks on Viscoelasticity of Polymer–Filler Nanocomposites: A Mesoscale Simulation Study

With nanoparticles (NPs) as fillers, polymer nanocomposites (PNCs) usually exhibit enhanced mechanical properties. However, a direct connection between the microscopic structural relaxation and macroscopic mechanical properties of PNCs remains to be established. To investigate the micro-to-macro connection, we develop a mesoscale model, in which the NPbridging polymer chains are represented by a dynamic bonded interaction between NPs, and the bulk polymer matrix is implicitly modeled by overdamped Langevin dynamics. Extensive equilibrium simulations are performed to quantify the microscopic dynamics of model PNCs. Systematic analyses of modified Rouse dynamics, dynamic structure factor, and relaxation modulus uncover that the microscopic relaxation dynamics of PNCs are significantly decelerated across different length scales because of nonlocal effects of percolated particle networks a phenomenon that has not been adequately captured in prior simulation studies. We find that NPvolume- fraction and NP-bonding-energy barrier are the two critical variables that affect bulk viscoelasticity the most. The proposed mesoscale model is versatile and provides a powerful framework for studying structure−property relations of different PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Using the Metropolis algorithm to explore the loss surface of a recurrent neural network

In the limit of small trial moves the Metropolis Monte Carlo algorithm is equivalent to gradient descent on the energy function in the presence of Gaussian white noise. This observation was originally used to demonstrate a correspondence between Metropolis Monte Carlo moves of model molecules and overdamped Langevin dynamics, but it also applies in the context of training a neural network: making small random changes to the weights of a neural network, accepted with the Metropolis probability, with the loss function playing the role of energy, has the same effect as training by explicit gradient descent in the presence of Gaussian white noise. We explore this correspondence in the context of a simple recurrent neural network. We also explore regimes in which this correspondence breaks down, where the gradient of the loss function becomes very large or small. In these regimes the Metropolis algorithm can still effect training, and so can be used as a probe of the loss function of a neural network in regimes in which gradient descent struggles. We also show that training can be accelerated by making purposely-designed Monte Carlo trial moves of neural-network weights.

Casert, Corneel↗
DOE OSTI2025

Improving noisy free-energy measurements by adding more noise

Estimating free-energy differences using nonequilibrium work relations, such as the Jarzynski equality, is hindered by poor convergence when work fluctuations are large. For systems governed by overdamped Langevin dynamics, we propose the counterintuitive approach of adding noise in order to increase the precision of such calculations. Here, by introducing additional stochastic fluctuations to the system and rescaling its potential energy accordingly, we leave the thermodynamics of the system unchanged while increasing its relaxation rate. For a given time-dependent protocol this modification reduces the dissipated reduced work, leading to more accurate free-energy estimates. The method is designed to be used in experiment, and we illustrate its operation using computer simulations applied to two model systems. However, the regime of applicability of this strategy is likely limited, because it requires control of the system's potential energy in a way that is feasible in only a few experimental settings.

Whitelam, Stephen [Lawrence Berkeley National Labo↗
DOE OSTI2020

Collective mode Brownian dynamics: A method for fast relaxation of statistical ensembles

Sampling equilibrium configurations of correlated systems of particles with long relaxation times (e.g., polymeric solutions) using conventional molecular dynamics and Monte Carlo methods can be challenging. This is especially true for systems with complicated, extended bond network topologies and other interactions that make the use and design of specialized relaxation protocols infeasible. We introduce a method based on Brownian dynamics simulations that can reduce the computational time it takes to reach equilibrium and draw decorrelated samples. Importantly, the method is completely agnostic to the particle configuration and the specifics of interparticle forces. In particular, we develop a mobility matrix that excites non-local, collective motion of N particles and can be computed efficiently in $\mathcal{O}(N)$ time. Particle motion in this scheme is computed by integrating the overdamped Langevin equation with an Euler–Maruyama scheme, in which Brownian displacements are drawn efficiently using a low-rank representation of the mobility matrix in position and wave space. We demonstrate the efficacy of the method with various examples from the realm of soft condensed matter and release a massively parallel implementation of the code as a plugin for the open-source package HOOMD-blue [J. A. Anderson et al., J. Comput. Phys. 227, 5342 (2008) and J. Glaser et al., Comput. Phys. Commun. 192, 97 (2015)] which runs on graphics processing units

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗