Abstract: Neural operators are a class of neural networks to learn mappings between infinite-dimensional function spaces, and recent studies have shown that using neural operators to solve partial ...

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. Once a well-suited model is established, it can be thoroughly ...

The Annals of Statistics, Vol. 48, No. 6 (December 2020), pp. 3336-3365 (30 pages) We consider N independent stochastic processes (Xi (t), t ∈ [0, T]), i = 1, . . . , N, defined by a one-dimensional ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...