Related papers: Anharmonic phonons with Gaussian processes
Excessive loads near wounds produce pathological scarring and other complications. Presently, stress cannot easily be measured by surgeons in the operating room. Instead, surgeons rely on intuition and experience. Predictive computational…
A non-perturbative algebraic theory of lattice Boltzmann method is developed based on a symmetry of a product. It involves three steps: (i) Derivation of admissible lattices in one spatial dimension through a matching condition which…
Lattice Boltzmann models are briefly introduced together with references to methods used to predict their ability for simulations of systems described by partial differential equations that are first order in time and low order in space…
Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work…
Gaussian Processes (GPs) are a class of kernel methods that have shown to be very useful in geoscience applications. They are widely used because they are simple, flexible and provide very accurate estimates for nonlinear problems,…
Knowledge of lattice anharmonicity is essential to elucidate distinctive thermal properties in crystalline solids. Yet, accurate \textit{ab initio} investigations of lattice anharmonicity encounter difficulties owing to the cumbersome…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…
Recent advances in analysis of subband amplitude envelopes of natural sounds have resulted in convincing synthesis, showing subband amplitudes to be a crucial component of perception. Probabilistic latent variable analysis is particularly…
For a learning task, Gaussian process (GP) is interested in learning the statistical relationship between inputs and outputs, since it offers not only the prediction mean but also the associated variability. The vanilla GP however struggles…
Surrogate models have shown to be an extremely efficient aid in solving engineering problems that require repeated evaluations of an expensive computational model. They are built by sparsely evaluating the costly original model and have…
In this paper, a novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics is developed for predicting the response of engineering systems and complex physical phenomena. The method utilizes…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Machine learning driven interatomic potentials, including Gaussian approximation potential (GAP) models, are emerging tools for atomistic simulations. Here, we address the methodological question of how one can fit GAP models that…
Gaussian processes (GPs) are widely used as surrogate models for complicated functions in scientific and engineering applications. In many cases, prior knowledge about the function to be approximated, such as monotonicity, is available and…
We present a review of recent work on the statistical mechanics of non equilibrium processes based on the analysis of large deviations properties of microscopic systems. Stochastic lattice gases are non trivial models of such phenomena and…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
Credible forecasting and representation learning of dynamical systems are of ever-increasing importance for reliable decision-making. To that end, we propose a family of Gaussian processes (GP) for dynamical systems with linear…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or…