Related papers: Latent Spaces for Langevin Dynamics
Several important learning tasks can be formulated as minimizing an entropy-regularized objective over an appropriate space of probability distributions. Mean-field Langevin dynamics (MFLD) facilitate computation in this general context,…
This article deals with the realisation of constraints in underdamped Langevin dynamics via soft-constrained dynamics. Specifically, we study systems with a large (or small) parameter that controls the constraint mechanisms, e.g. the…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
By exact projection in phase space we derive the generalized Langevin equation (GLE) for time-filtered observables. We employ a general convolution filter that directly acts on arbitrary phase-space observables and can involve low-pass,…
Bottom-up coarse-grained molecular dynamics models are parameterized using complex effective Hamiltonians. These models are typically optimized to approximate high dimensional data from atomistic simulations. In contrast, human validation…
We present a Langevin approach to describe the steady-state dynamics of one-dimensional granular media fluidized by a vibrating bottom plate. We adopt a linear Langevin equation to describe the motion of the center of mass. Within this…
Ion channels are important proteins for physiological information transfer and functional control. To predict the microscopic origins of their voltage-conductance characteristics, we here applied dissipation-corrected targeted Molecular…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
Minimizing non-convex and high-dimensional objective functions is challenging, especially when training modern deep neural networks. In this paper, a novel approach is proposed which divides the training process into two consecutive phases…
These short notes present to the reader (students, in particular) a concise approach to the derivation of the propagator of Hamiltonians with position-dependent kinetic energy. The formalism is applied to the von Roos Hamiltonian with…
Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
Sampling is a fundamental and arguably very important task with numerous applications in Machine Learning. One approach to sample from a high dimensional distribution $e^{-f}$ for some function $f$ is the Langevin Algorithm (LA). Recently,…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
Latent variable models are powerful tools for learning low-dimensional manifolds from high-dimensional data. However, when dealing with constrained data such as unit-norm vectors or symmetric positive-definite matrices, existing approaches…
Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or…
We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary…
In this paper we introduce and analyse Langevin samplers that consist of perturbations of the standard underdamped Langevin dynamics. The perturbed dynamics is such that its invariant measure is the same as that of the unperturbed dynamics.…
Quantum state processing is one of the main tools of quantum technologies. While real systems are complicated and/or may be driven by non-ideal control they may nevertheless exhibit simple dynamics approximately confined to a low-energy…
Coarse-grained molecular dynamics often sacrifices accuracy and transferability for computational efficiency, but the use of machine learned potentials is helping coarse-grained models attain performance on par with atomistic molecular…