The University of Tokyo · Mathematics
Professor Takashi Goda's research lab specializes in computational mathematics and uncertainty quantification, with a focus on high-dimensional integration, quasi-Monte Carlo methods, and stochastic optimization. The lab develops advanced numerical algorithms—particularly median-based and multilevel Monte Carlo techniques—for efficient and accurate integration in weighted function spaces, including Korobov and Sobolev spaces with arbitrary smoothness. A key research direction involves constructing provably optimal QMC rules using digital nets and polynomial lattice rules, while also addressing challenges in Bayesian experimental design and CO₂ geological storage simulations. The lab bridges theoretical analysis with practical applications in environmental modeling and scientific computing.
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We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the multidimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new construction-free median QMC rule which can exploit the smoothness and the weights of function spaces adaptively. For weighted Korobov spaces, we draw a sample of $r$ independent generating vectors of rank-1 lattice rules, compute the integral estimate for each, and approximate the true integral by the median of these $r$ estimate
Optimization of injection well placement deserves careful and thoughtful consideration to achieve the higher safety of CO2 geological storage. In this study, a storage safety is quantified as a proportion of the immobile and dissolved CO2 to the total injected amount. Here we revisit the definition of immobile CO2 from a standpoint of long-term CO2 migration. Owing to the irreversibility of relative permeability curves, a fraction of CO2 which is displacing brine will eventually become trapped a
We investigate quasi-Monte Carlo integration using higher order digital nets in weighted Sobolev spaces of arbitrary fixed smoothness α∈ℕ, α≥2, defined over the s-dimensional unit cube. We prove that randomly digitally shifted order β digital nets can achieve the convergence of the root mean square worst-case error of order N−α(logN)(s−1)/2 when β≥2α. The exponent of the logarithmic term, i.e., (s−1)/2, is improved compared to the known result by Baldeaux and Dick, in which the exponent is s
In this paper we propose an efficient stochastic optimization algorithm to search for Bayesian experimental designs such that the expected information gain is maximized. The gradient of the expected information gain with respect to experimental design parameters is given by a nested expectation, for which the standard Monte Carlo method using a fixed number of inner samples yields a biased estimator. In this paper, applying the idea of randomized multilevel Monte Carlo (MLMC) methods, we introdu
In the geological sequestration of carbon dioxide (CO 2 ), residual gas trapping plays an important role in immobilizing CO 2 . In this study, we investigate the propagation of gravity currents with residual gas trapping in a two-layered porous medium. We first formulate a model for a constant-flux release of a relatively less dense fluid (CO 2 ) from a point source into a porous medium bounded above by a horizontal less-permeable seal. After a constant-flux release ceases, a fraction of the rel
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