arXiv subjects

Rodrigo A. Vargas-Hernández

Publications and source records attributed to Rodrigo A. Vargas-Hernández.

23 records · Page 2Linked to original sources

arXiv2021

Multi-objective optimization for retinal photoisomerization models with respect to experimental observables

The fitting of physical models is often done only using a single target observable. However, when multiple targets are considered, the fitting procedure becomes cumbersome, there being no easy way to quantify the robustness of the model for all different observables. Here, we illustrate that one can jointly search for the best model for each desired observable through multi-objective optimization. To do so we construct the Pareto front to study if there exists a set of parameters of the model that can jointly describe multiple, or all, observables. To alleviate the computational cost, the predicted error for each targeted objective is approximated with a Gaussian process model, as it is commonly done in the Bayesian optimization framework. We applied this methodology to improve three different models used in the simulation of stationary state $cis-trans$ photoisomerization of retinal in rhodopsin. Optimization was done with respect to different experimental measurements, including emission spectra, peak absorption frequencies for the $cis$ and $trans$ conformers, and the energy storage.

physics.chem-ph↗

arXiv2020

Inverse design of dissipative quantum steady-states with implicit differentiation

Inverse design of a property that depends on the steady-state of an open quantum system is commonly done by grid-search type of methods. In this paper we present a new methodology that allows us to compute the gradient of the steady-state of an open quantum system with respect to any parameter of the Hamiltonian using the implicit differentiation theorem. As an example, we present a simulation of a spin-boson model where the steady-state solution is obtained using Redfield theory.

quant-ph↗

arXiv2019

Bayesian optimization for tuning and selecting hybrid-density functionals

The accuracy of some density functional (DF) models, widely used in material science, depends on empirical or free parameters which are commonly tuned using reference physical properties. The optimal value of the free parameters is regularly found using grid search algorithms, which computational complexity scales with the number of points in the grid. In this report, we illustrate that Bayesian optimization (BO), a sample-efficient machine learning algorithm, can efficiently calibrate different density functional models, e.g., hybrid-exchange-correlation and range-separated density functionals. We present that, BO can optimize the free parameters of hybrid-exchange-correlation functionals, with approximately 55 evaluations of the root-mean-square or mean-absolute error functions of the atomization energies and the bond length of the Gaussian-1 (G1) database. We also illustrate that BO can identify, without any prior information, the most appropriate exchange-correlation functional by navigating through the space of density functional models. We optimize and select the free parameters and the exchange-correlation functional form jointly by also minimizing the root-mean-square error function with respect to the atomization energies of the G1 database using BO.

physics.comp-ph↗

arXiv2019

Physical extrapolation of quantum observables by generalization with Gaussian Processes

For applications in chemistry and physics, machine learning (ML) is generally used to solve one of three problems: interpolation, classification or clustering. These problems use information about physical systems in a certain range of parameters or variables in order to make predictions at unknown values of these variables within the same range. The present work illustrates the application of ML to prediction of physical properties outside the range of the training parameters. We define `physical extrapolation' to refer to accurate predictions $y(\mathbf{x^\ast})$ of a given physical property at a point $\mathbf{x^\ast} = [ x^\ast_1, ..., x^\ast_{\cal D} ]$ in the $\cal D$-dimensional space, if, at least, one of the variables $x^\ast_i \in \left [ x^\ast_1, ..., x^\ast_{\cal D} \right ]$ is {\it outside} of the range covering the training data. We show that Gaussian processes (GPs) can be used to build ML models capable of physical extrapolation of quantum properties of complex systems across quantum phase transitions. The approach is based on training GP models of variable complexity by the evolution of the physical functions. We show that, as the complexity of the models increases, they become capable of predicting new transitions. We also show that, where the evolution of the physical functions is analytic and relatively simple, GP models with simple kernels already yield accurate generalization results, allowing for accurate predictions of quantum properties in a different quantum phase. For more complex problems, it is necessary to build models with complex kernels. The complexity of the kernels is increased using the Bayesian Information Criterion (BIC). We illustrate the importance of the BIC by comparing the results with random kernels of various complexity and illustrate a method to obtain meaningful extrapolation results without direct validation in the extrapolated region.

physics.comp-ph↗

arXiv2019

Extrapolating quantum observables with machine learning: Inferring multiple phase transitions from properties of a single phase

We present a machine-learning method for predicting sharp transitions in a Hamiltonian phase diagram by extrapolating the properties of quantum systems. The method is based on Gaussian Process regression with a combination of kernels chosen through an iterative procedure maximizing the predicting power of the kernels. The method is capable of extrapolating across the transition lines. The calculations within a given phase can be used to predict not only the closest sharp transition, but also a transition removed from the available data by a separate phase. This makes the present method particularly valuable for searching phase transitions in the parts of the parameter space that cannot be probed experimentally or theoretically.

cond-mat.other↗