Deep Learning Approach to Partial Differential Equations | Leah Bar, OriginAI (PyData TLV June22)

Introducing a novel deep learning approach to solving partial differential equations without labeled data, using a simple neural network that can accurately reproduce ground truth.

Key takeaways

The speaker introduce a deep learning approach to solving partial differential equations (PDEs).
The approach focuses on unsupervised learning, unlike traditional methods which require labeled data.
The neural network model used is a simple multilayer perceptron (MLP) with a few layers and hyperbolic tangent activation.
The model does not require discretization of the domain, allowing it to handle complex shapes and arbitrary domains.
The approach is demonstrated through examples, including a 1D problem, a 2D problem, and a 3D problem.
The results show that the approach can accurately solve PDEs and reproduce the ground truth.
The speaker notes that the L2 norm is not sufficient for PDEs, and that the L∞ norm is more effective in reducing errors.
The approach is fast and efficient, requiring only a few lines of code.
The speaker also discusses the connection to other fields, such as biomedical engineering and image processing.
The approach can be extended to nonlinear problems and high-dimensional problems.
The speaker mentions that the method is mesh-free and does not require manual discretization of the domain.
The approach can also be used for inverse problems, where the goal is to find the coefficients of a PDE given the solution.
The speaker notes that the approach is self-supervised and does not require labeled data.

Deep Learning Approach to Partial Differential Equations | Leah Bar, OriginAI (PyData TLV June22)

More talks