arXiv research

Deep neural networks improve free energy calculations for peptide conformations.

FEAT estimates free energy using adaptive transports.

Novel ML model predicts solvation free energies from atom interactions.

Enhanced diffusion sampling improves rare event sampling in biomolecular simulations.

Enhanced diffusion sampling tackles rare event sampling in biomolecular simulations.

Paper proposes energy objective for training normalizing flows without determinants.

We calculate the free energy of Coulomb gas systems on Riemann surfaces.

The inference of correlated signal fields with unknown correlation structures is of high scientific and technological relevance, but poses significant conceptual and numerical challenges. To address these, we develop the correlated signal inference (CSI) algorithm within information field theory (IFT) and discuss its n…

We propose to learn deep undirected graphical models (i.e., MRFs) with a non-ELBO objective for which we can calculate exact gradients. In particular, we optimize a saddle-point objective deriving from the Bethe free energy approximation to the partition function. Unlike much recent work in approximate inference, the d…

We translate the problem of calculating the entropy of a set of binary configurations/signals into a sequence of supervised classification tasks. Subsequently, one can use virtually any machine learning classification algorithm for computing entropy. This procedure can be used to compute entropy, and consequently the f…

Sharp stability in Almgren problem solved in any dimension.

The paper proves a disk's energy minimizer is holomorphic and calculates its Morse index.

The heuristic identification of peaks from noisy complex spectra often leads to misunderstanding of the physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multipeak spectra into single peaks statistically and consists of two steps.…

Developed accurate empirical potentials for Si:H nanowires using multi-fidelity Gaussian process.

The calculation of minimum energy paths for transitions such as atomic and/or spin re-arrangements is an important task in many contexts and can often be used to determine the mechanism and rate of transitions. An important challenge is to reduce the computational effort in such calculations, especially when ab initio …

The paper studies geometric properties of hydrodynamical density manifolds.

A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus…

Geometry of hypersurfaces defined by the relation which generalizes classical formula for free energy in terms of microstates is studied. Induced metric, Riemann curvature tensor, Gauss-Kronecker curvature and associated entropy are calculated. Special class of ideal statistical hypersurfaces is analyzed in details. No…

Researchers created an accurate kinetic energy functional for materials modeling.

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where an initial path is iteratively shifted to the nearest minimum energy path. The co…

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases o…

The two-dimensional renormalization group acting as the Ricci flow $Λ\frac{\partial}{\partialΛ} g_{μν} = R_{μν}$ produces a specific 1+3 dimensional space-time metric which describes an expanding universe that starts with a big bang $a \sim t^{\scriptscriptstyle 1/\sqrt3}$ then decelerates until $z=0.2$ then accelerate…

mAIS improves free energy evaluation efficiency.

We use matricial free energy to regularize autoencoders, producing Gaussian-like codes.

Study on existence of ground states for free energy on hyperbolic space.

New result on critical points of Bethe free energy under deformation retracts.

New model estimates Gibbs free energies using machine learning and isobaric-isothermal flows.

Study of phase separation and geometry on a closed elastic curve, including dynamics and free energy minimization.

Active inference minimizes expected free energy for optimal behavior.

Paper analyzes the free energy of CNNs with skip connections in Bayesian learning.

Proposes a new quasi-local mass for timelike 2-surfaces in spacetimes.

New method uses neural networks to improve free energy estimation.

A neural network model minimizes region-based free energy for faster inference in MRFs.

Following the thermodynamic formulation of multifractal measure that was shown to be capable of detecting large fluctuations at an early stage, here we propose a new index which permits us to distinguish events like financial crisis in real time . We calculate the partition function from where we obtain thermodynamic q…

We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Beth…

Study finds surfaces in spherical caps that maximize modified energy.

We will give a weak energy identity for Sacks-Uhlenbeck approximation of harmonic maps and calculate the length of the necks.

Study free energy in spherical spin glasses, proving universality dichotomy.

Paper improves zero-shot protein stability prediction by clarifying free-energy foundations.

Unified framework for planning under uncertainty using variational inference.

This paper generalizes neural transport learning for free energy estimation in arbitrary state spaces.

New algorithms learn latent variable models without tuning, outperforming existing methods.

Ownership cost calculation plays an important role in optimal operation of distributed energy resources (DERs) and microgrids (MGs) in the future power system, known as smart grid. In this paper, a general framework for ownership cost calculation is proposed using uncertainty and risk analyses. Four ownership cost calc…

The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a …

The free energy functional has recently been proposed as a variational principle for bounded rational decision-making, since it instantiates a natural trade-off between utility gains and information processing costs that can be axiomatically derived. Here we apply the free energy principle to general decision trees tha…

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approach…

Active learning reduces SP calculations by 90%.

Straight lines are a basin of attraction for the elastic flow at least to level 1.9615π.