Dataset Information

Energy Derivatives in Real-Space Diffusion Monte Carlo.

ABSTRACT: We present unbiased, finite-variance estimators of energy derivatives for real-space diffusion Monte Carlo calculations within the fixed-node approximation. The derivative d_λE is fully consistent with the dependence E(λ) of the energy computed with the same time step. We address the issue of the divergent variance of derivatives related to variations of the nodes of the wave function both by using a regularization for wave function parameter gradients recently proposed in variational Monte Carlo and by introducing a regularization based on a coordinate transformation. The essence of the divergent variance problem is distilled into a particle-in-a-box toy model, where we demonstrate the algorithm.

SUBMITTER: van Rhijn J

PROVIDER: S-EPMC8757439 | biostudies-literature | 2022 Jan

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Energy Derivatives in Real-Space Diffusion Monte Carlo.

van Rhijn Jesse J Filippi Claudia C De Palo Stefania S Moroni Saverio S

Journal of chemical theory and computation 20211220 1

We present unbiased, finite-variance estimators of energy derivatives for real-space diffusion Monte Carlo calculations within the fixed-node approximation. The derivative dλE is fully consistent with the dependence E(λ) of the energy computed with the same time step. We address the issue of the divergent variance of derivatives related to variations of the nodes of the wave function both by using a regularization for wave function parameter gradients recently proposed i ...[more]

PMID: 34930005

Similar Datasets

Project description:In diffusion MRI analysis, advances in biophysical multi-compartment modeling have gained popularity over the conventional Diffusion Tensor Imaging (DTI), because they can obtain a greater specificity in relating the dMRI signal to underlying cellular microstructure. Biophysical multi-compartment models require a parameter estimation, typically performed using either the Maximum Likelihood Estimation (MLE) or the Markov Chain Monte Carlo (MCMC) sampling. Whereas, the MLE provides only a point estimate of the fitted model parameters, the MCMC recovers the entire posterior distribution of the model parameters given in the data, providing additional information such as parameter uncertainty and correlations. MCMC sampling is currently not routinely applied in dMRI microstructure modeling, as it requires adjustment and tuning, specific to each model, particularly in the choice of proposal distributions, burn-in length, thinning, and the number of samples to store. In addition, sampling often takes at least an order of magnitude, more time than non-linear optimization. Here we investigate the performance of the MCMC algorithm variations over multiple popular diffusion microstructure models, to examine whether a single, well performing variation could be applied efficiently and robustly to many models. Using an efficient GPU-based implementation, we showed that run times can be removed as a prohibitive constraint for the sampling of diffusion multi-compartment models. Using this implementation, we investigated the effectiveness of different adaptive MCMC algorithms, burn-in, initialization, and thinning. Finally we applied the theory of the Effective Sample Size, to the diffusion multi-compartment models, as a way of determining a relatively general target for the number of samples needed to characterize parameter distributions for different models and data sets. We conclude that adaptive Metropolis methods increase MCMC performance and select the Adaptive Metropolis-Within-Gibbs (AMWG) algorithm as the primary method. We furthermore advise to initialize the sampling with an MLE point estimate, in which case 100 to 200 samples are sufficient as a burn-in. Finally, we advise against thinning in most use-cases and as a relatively general target for the number of samples, we recommend a multivariate Effective Sample Size of 2,200.

Dataset Information

Energy Derivatives in Real-Space Diffusion Monte Carlo.

Publications

Energy Derivatives in Real-Space Diffusion Monte Carlo.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets