The University of Tokyo · 수학
타카시 고다 교수의 연구실은 고차원 통합 및 수치적 통계 방법을 중심으로 한 응용 수학과 계산 과학 분야에서 활발히 연구를 진행하고 있습니다. 주요 연구 방향은 고차원 함수 공간에서의 준몬테카를로(QMC) 통합 기법, 특히 스무딩 성질과 가중치를 자동으로 적응적으로 활용하는 중앙값 기반 QMC 규칙 및 고순서 디지털 넷의 오차 수렴 속도 향상에 초점이 맞춰져 있습니다. 또한, 지속 가능한 에너지 기술과 관련된 지구 저장 문제, 예를 들어 CO₂ 갇힘 및 지하 저장 안정성 분석에도 응용 연구를 펼치고 있습니다. 이는 수치 해석과 확률적 최적화의 융합을 통해 실제 문제 해결에 기여하는 응용 중심의 연구 철학을 반영합니다.
표시된 성과는 수집된 데이터 기준으로 산출되며, 일부 차이가 있을 수 있습니다.
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
