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What's Changed Hpc stabilize by @alegresor in https://github.com/QMCSoftware/QMCSoftware/pull/382 Update README.md by @zitterbewegung in https://github.com/QMCSoftware/QMCSoftware/pull/385 Geometric brownian motion by @larissensium in https://github.com/QMCSoftware/QMCSoftware/pull/392 QMCPy Overhaul by @alegresor in https://github.com/QMCSoftware/QMCSoftware/pull/391 v2.0 by @alegresor in https://github.com/QMCSoftware/QMCSoftware/pull/394 New Contributors @larissensium made their first contribution in https://github.com/QMCSoftware/QMCSoftware/pull/392 Full Changelog: https://github.com/QMCSoftware/QMCSoftware/compare/v1.6.1...v2.0 

Limiting the injection rate to restrict the pressure below a threshold at a critical location can be an important goal of simulations that model the subsurface pressure between injection and extraction wells. The pressure is approximated by the solution of Darcy’s partial differential equation for a given permeability field. The subsurface permeability is modeled as a random field since it is known only up to statistical properties. This induces uncertainty in the computed pressure. Solving the partial differential equation for an ensemble of random permeability simulations enables estimating a probability distribution for the pressure at the critical location. These simulations are computationally expensive, and practitioners often need rapid online guidance for real-time pressure management. An ensemble of numerical partial differential equation solutions is used to construct a Gaussian process regression model that can quickly predict the pressure at the critical location as a function of the extraction rate and permeability realization. The Gaussian process surrogate analyzes the ensemble of numerical pressure solutions at the critical location as noisy observations of the true pressure solution, enabling robust inference using the conditional Gaussian process distribution. Our first novel contribution is to identify a sampling methodology for the random environment and matching kernel technology for which fitting the Gaussian process regression model scales as O(nlog 𝑛) instead of the typical O(𝑛^3 ) rate in the number of samples 𝑛 used to fit the surrogate. The surrogate model allows almost instantaneous predictions for the pressure at the critical location as a function of the extraction rate and permeability realization. Our second contribution is a novel algorithm to calibrate the uncertainty in the surrogate model to the discrepancy between the true pressure solution of Darcy’s equation and the numerical solution. Although our method is derived for building a surrogate for the solution of Darcy’s equation with a random permeability field, the framework broadly applies to solutions of other partial differential equations with random coefficients. 

A large literature specifies conditions under which the information complexity for a se- quence of numerical problems defined for dimensions 1, 2, . . . grows at a moderate rate, i.e., the sequence of problems is tractable. Here, we focus on the situation where the space of available information consists of all linear functionals, and the problems are defined as lin- ear operator mappings between Hilbert spaces. We unify the proofs of known tractability results and generalize a number of existing results. These generalizations are expressed as five theorems that provide equivalent conditions for (strong) tractability in terms of sums of functions of the singular values of the solution operators.