Related papers: Metadynamics with adaptive Gaussians
Finite mixture of Gaussian distributions provide a flexible semi-parametric methodology for density estimation when the variables under investigation have no boundaries. However, in practical applications variables may be partially bounded…
The process of calibrating computer models of natural phenomena is essential for applications in the physical sciences, where plenty of domain knowledge can be embedded into simulations and then calibrated against real observations. Current…
The theoretical investigation of gas adsorption, storage, separation, diffusion and related transport processes in porous materials relies on a detailed knowledge of the potential energy surface of molecules in a stationary environment. In…
Solvent plays an important role in the relative motion of nanoscopic bodies, and the study of such phenomena can help elucidate the mechanism of hydrophobic assembly, as well as the influence of solvent-mediated effects on in vivo motion in…
We develop a formulation of global thermodynamics for equilibrium systems under the influence of gravity. The free energy for simple fluids is extended to include a dependence on $(T, V, N, mgL)$, where $L$ represents the vertical system…
3D Gaussian Splatting (3DGS) has become an emerging tool for dynamic scene reconstruction. However, existing methods focus mainly on extending static 3DGS into a time-variant representation, while overlooking the rich motion information…
This report presents the application of polynomial regression for estimating free energy differences using thermodynamic integration. We employ linear regression to construct a polynomial that optimally fits the thermodynamic integration…
Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…
We introduce Adjoint Sampling, a highly scalable and efficient algorithm for learning diffusion processes that sample from unnormalized densities, or energy functions. It is the first on-policy approach that allows significantly more…
Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an…
Slow adaption processes, like synaptic and intrinsic plasticity, abound in the brain and shape the landscape for the neural dynamics occurring on substantially faster timescales. At any given time the network is characterized by a set of…
An energy-biased method to evaluate ensemble averages requiring test-particle insertion is presented. The method is based on biasing the sampling within the subdomains of the test-particle configurational space with energies smaller than a…
We present a calculation of the change of free energy of a solid surface upon bending of the solid. It is based on extracting the surface stress through a molecular dynamics simulation of a bent slab by using a generalized stress theorem…
We introduce a novel scheme for the mechanistic investigation of solid-solid phase transitions, which we dub \textit{metashooting}. Combining transition path sampling molecular dynamics and metadynamics, this scheme allows for both a…
We consider the statistical mechanics of a classical particle in a one-dimensional box subjected to a random potential which constitutes a Wiener process on the coordinate axis. The distribution of the free energy and all correlation…
In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…
We consider the governing equations for the motion of compressible fluid on an evolving surface from both energetic and thermodynamic points of view. We employ our energetic variational approaches to derive the momentum equation of our…
Recent advances in artificial intelligence have been fueled by the development of foundation models such as BERT, GPT, T5, and Vision Transformers. These models are first pretrained on vast and diverse datasets and then adapted to specific…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…