About Diogo Gomes Diogo Gomes Professor, Applied Mathematics and Computational Science mean-field games Hamilton-Jacobi equations nonlinear PDEs Professor Diogo Gomes, a distinguished expert in Applied Mathematics and Computational Science at KAUST, leverages advanced mathematics – including partial differential equations, numerical methods and mean-field game models – to solve complex problems in social sciences, economics and finance Events Presented Events Nov 26 - Dec 2, 2023 Derivative-Free Global Minimization: Relaxation, Monte Carlo and Sampling Diogo Gomes, Professor, Applied Mathematics and Computational Science Nov 27, 11:30 - 12:30 B9 L2 H2 H2 minimization Gradient flows Monte Carlo Monte Carlo Methodology We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small. Oct 1 - Oct 7, 2023 How many sample points do we need for least squares? Diogo Gomes, Professor, Applied Mathematics and Computational Science Oct 5, 12:00 - 13:00 B9 L2 H2 Abstract The goal of the least squares method is to find the best linear combination of certain given functions to fit given data. A typical example is the following: given pairs $(x_i, y_i)$, find the coefficients, $a$ and $b$ that minimize the error $\sum_i (y_i-a -b x_i)^2$. In this case, if at least two of the coordinates $x_i$ are distinct, we can always find coefficients $a$ and $b$. However, if the $x_i$ are randomly sampled, these coordinates may be extremely close, creating large errors in the estimated values of $a$ and $b$. In this talk, we investigate lower bounds on the minimum Jan 30 - Feb 5, 2022 New tools for symbolic computation in partial differential equations Diogo Gomes, Professor, Applied Mathematics and Computational Science Jan 31, 12:00 - 13:00 KAUST The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness. Oct 24 - Oct 30, 2021 Recent progress on symbolic computation for PDE and their numerical schemes Diogo Gomes, Professor, Applied Mathematics and Computational Science Oct 28, 12:00 - 13:00 KAUST The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness. Nov 3 - Nov 9, 2019 On mean-field game price models Diogo Gomes, Professor, Applied Mathematics and Computational Science Nov 7, 12:00 - 13:00 B9 L2 H1 R2322 mean-field games price formation modeling linear-quadratic problem optimal transport with constraints supply and demand balance Abstract In this talk, we discuss a mean-field game price formation model. This model describes a large number of rational agents that can trade a commodity with an exogenous supply. The price is determined by a balance condition between supply and demand. We discuss the well-posedness of the model, the uniqueness and regularity of the price function. Then, we examine two explicit models - the linear-quadratic problem and a model with finitely many agents. Time permitting, we will examine the connections between this problem and optimal transport with constraints. Brief Biography Diogo Gomes
Derivative-Free Global Minimization: Relaxation, Monte Carlo and Sampling Diogo Gomes, Professor, Applied Mathematics and Computational Science Nov 27, 11:30 - 12:30 B9 L2 H2 H2 minimization Gradient flows Monte Carlo Monte Carlo Methodology We develop a derivative-free global minimization algorithm that is based on a gradient flow of a relaxed functional. We combine relaxation ideas, Monte Carlo methods, and resampling techniques with advanced error estimates. Compared with well-established algorithms, the proposed algorithm has a high success rate in a broad class of functions, including convex, non-convex, and non-smooth functions, while keeping the number of evaluations of the objective function small.
How many sample points do we need for least squares? Diogo Gomes, Professor, Applied Mathematics and Computational Science Oct 5, 12:00 - 13:00 B9 L2 H2 Abstract The goal of the least squares method is to find the best linear combination of certain given functions to fit given data. A typical example is the following: given pairs $(x_i, y_i)$, find the coefficients, $a$ and $b$ that minimize the error $\sum_i (y_i-a -b x_i)^2$. In this case, if at least two of the coordinates $x_i$ are distinct, we can always find coefficients $a$ and $b$. However, if the $x_i$ are randomly sampled, these coordinates may be extremely close, creating large errors in the estimated values of $a$ and $b$. In this talk, we investigate lower bounds on the minimum
New tools for symbolic computation in partial differential equations Diogo Gomes, Professor, Applied Mathematics and Computational Science Jan 31, 12:00 - 13:00 KAUST The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness.
Recent progress on symbolic computation for PDE and their numerical schemes Diogo Gomes, Professor, Applied Mathematics and Computational Science Oct 28, 12:00 - 13:00 KAUST The qualitative study of PDEs often relies on integral identities and inequalities. For example, for time-dependent PDEs, conserved integral quantities or quantities that are dissipated play an important role. In particular, if these integral quantities have a definite sign, they are of great interest as they may provide control on the solutions to establish well-posedness.
On mean-field game price models Diogo Gomes, Professor, Applied Mathematics and Computational Science Nov 7, 12:00 - 13:00 B9 L2 H1 R2322 mean-field games price formation modeling linear-quadratic problem optimal transport with constraints supply and demand balance Abstract In this talk, we discuss a mean-field game price formation model. This model describes a large number of rational agents that can trade a commodity with an exogenous supply. The price is determined by a balance condition between supply and demand. We discuss the well-posedness of the model, the uniqueness and regularity of the price function. Then, we examine two explicit models - the linear-quadratic problem and a model with finitely many agents. Time permitting, we will examine the connections between this problem and optimal transport with constraints. Brief Biography Diogo Gomes
Engage ORCID KAUST Repository KAUST Academic Portal Scopus ShareClipboard Related Sites Applied Mathematics and Computational Science (AMCS) Center of Excellence for Generative AI (GenAI) Advances in nonlinear elliptic and parabolic pdes (NLPDES) Mean-field Games and Nonlinear PDE (MFG) Events Mean Field Games: From Many-Player Games to PDEs Melih Ucer, Postdoctoral Research Fellow, Applied Mathematics and Computational Science Dec 11, 12:00 - 13:00 B9, L2, R2325 mean field games hamilton–jacobi equations monotone operator theory Related Content Articles 6 Events 5
Mean Field Games: From Many-Player Games to PDEs Melih Ucer, Postdoctoral Research Fellow, Applied Mathematics and Computational Science Dec 11, 12:00 - 13:00 B9, L2, R2325 mean field games hamilton–jacobi equations monotone operator theory
