Yudovich Theory for Rough Path Perturbations of Euler's Equation - Lecture 5
Explore Yudovich Theory for rough path perturbations of Euler's equation, delving into advanced fluid dynamics concepts and mathematical techniques.
Yudovich Theory for Rough Path Perturbations of Euler's Equation - Lecture 4
Explore Yudovich Theory for rough path perturbations of Euler's equation, delving into advanced fluid dynamics concepts and mathematical techniques for analyzing fluid flow.
A Short but Up-to-Date Introduction to Partially Parabolic Systems - Lecture 4
Explore advanced concepts in fluid mechanics, focusing on Euler and Navier-Stokes equations. Gain insights into recent breakthroughs and cutting-edge techniques in this field of mathematical physics.
Modeling Electromagnetics with Partial Differential Equations - Part 1: Electrostatics
Formulate and solve electrostatic PDE models, focusing on interpolation of discontinuous quantities and exploring a multiphysics actuator application.
Modeling Fluid Dynamics with Navier-Stokes Equations
Explore fluid flow modeling using partial differential equations and learn to solve Navier-Stokes equations with NDSolve.
Solving PDEs in Matlab Using FFT
Learn to solve partial differential equations efficiently using Fast Fourier Transform in MATLAB, enhancing your engineering mathematics skills for advanced problem-solving.
A Deep Learning Scheme for Solving Fully Nonlinear Partial Differential Equations
Discover how deep learning algorithms converge to solve complex nonlinear PDEs, with applications in optimal investment problems and transaction cost analysis in financial mathematics.
Machine Learning for Computational Fluid Dynamics
Explore machine learning's potential to enhance computational fluid dynamics, covering applications in simulations, turbulence modeling, and reduced-order models while emphasizing physics-informed approaches.
Deep Learning to Discover Coordinates for Dynamics - Autoencoders & Physics Informed Machine Learning
Explore deep learning techniques for discovering effective coordinate systems in dynamical systems, enabling simpler models and physical law discovery. Focus on autoencoders and physics-informed machine learning.
DeepSet and Derivative Networks for Solving Symmetric Problems
Explore DeepSet networks for solving symmetric problems in high-dimensional PDEs and control, with applications in finance and mean-field control. Learn about their advantages and performance in various scenarios.
Vectorization, Decomposition, and PDE Identification in Imaging and Inverse Problems
Explore image vectorization, decomposition, and PDE identification techniques. Learn about silhouette extraction, image separation, and differential equation recovery from discrete data.
The Mathematics of Artificial Intelligence
Explore the mathematical foundations of AI, its impact on problem-solving in mathematics, and the challenges in developing reliable AI systems. Gain insights into generalization, explainability, and AI applications in inverse problems and PDEs.
Introduction to Optimal Transportation and Monge Ampère Type Equations - Lecture 2
Explore optimal transportation and Monge Ampère equations, covering key concepts like super differentials, isoperimetric problems, and probability measures in this advanced mathematics lecture.
Optimal Transportation, Monge-Ampère Equations and Riemannian Ricci Bounds - Lecture 1
Explore optimal transportation, Monge-Ampère equations, and Riemannian Ricci bounds in this advanced mathematics lecture by L. Ambrosio from Scuola Normale Superiore di Pisa.
New Approaches in Simulation of Transition Paths - IPAM at UCLA
Explores tensor methods for simulating chemical transition processes, focusing on compressing high-dimensional PDE functions and introducing a novel tensor-network generative modeling approach without optimization.
Wasserstein GANs Work Because They Fail - to Approximate the Wasserstein Distance
Explore the counterintuitive success of Wasserstein GANs despite their failure to accurately approximate the Wasserstein distance, offering insights into their effectiveness in generative modeling.
Deep Learning Approaches in Inverse Problems by Deep Ray
Explore deep learning techniques for solving inverse problems in various fields, focusing on applications, challenges, and recent advancements in this cutting-edge area of research.
Normalization Effects on Neural Networks: Generalization and High-Dimensional Applications - SIAM FME Talk
Exploring neural network performance, normalization effects, and high-dimensional PDE solving using deep learning. Insights on generalization properties and applications in mathematical finance.
Converging Advances to Accelerate Molecular Simulation
Explore advances in molecular simulation through deep learning, ASIC architectures, and quantum computation. Discover potential applications in sustainable technologies, drug development, and material design.
GenPhys: From Physical Processes to Generative Models
Explore how physical processes inspire new generative models, including diffusion and Poisson flow. Learn to translate PDEs into AI algorithms and expand the design space of generative approaches.
Math for Game Programmers - Harmonic Functions and Mean-Value
Explore harmonic functions and mean-value parameterizations for procedural geometry in game development, with applications in mesh manipulation and UV generation.