Samuel Burbulla
Samuel is an applied mathematician who pursued his PhD in mathematical modelling and numerical simulation. Now, he is enthusiastic about everything that makes machines intelligent! In particular, he is interested in the application of machine learning to the simulation of physical systems. This involves physics-informed deep neural networks, operator learning and other approaches to scientific ML.

Samuel's work

Pill

Mesh-Independent Operator Learning for Partial Differential Equations

The mesh-independent neural operator (MINO) is a fully attentional architecture for operator learning that allows to represent the …

Samuel Burbulla
Simulation and AI
Pill

Deep neural operators as accurate surrogates for shape optimization

Deep neural operators, such as DeepONet, have changed the paradigm in high-dimensional nonlinear regression, promising significant …

Samuel Burbulla
Simulation and AI
Software

continuiti: Learning Function Operators with Neural Networks

continuiti is a Python package for machine learning on function operators. It implements various neural operator architectures (e.g., …

Samuel Burbulla Jakob Wagner
Simulation and AI
Pill

BelNet: Basis-enhanced learning network

Operator learning trains a neural network to map functions to functions. An ideal operator learning framework should not require a …

Samuel Burbulla
Simulation and AI
Seminar

Learning Function Operators with Neural Networks

Samuel Burbulla, Senior AI Researcher at appliedAI Institute, will give an overview of recent advances in operator learning and their …

Samuel Burbulla
Simulation and AI
Pill

GraphCast: The Hidden Revolution of Numerical Weather Prediction

Traditional models for numerical weather prediction are inherently complex and require significant computational resources. GraphCast is a …

Samuel Burbulla
Simulation and AI
Pill

Neural Operators: Learning Maps Between Function Spaces

Neural operators are generalized neural networks that can map between infinite dimensional function spaces. A recent paper proposes a …

Samuel Burbulla
Simulation and AI
Blog

FLAME 2023: Diving into the Future of Fluid Dynamics and Machine Learning

At the Stanford FLAME AI Workshop 2023, I immersed myself in the intersection of machine learning and fluid dynamics, benefiting from …

Samuel Burbulla
Simulation and AI
Pill

Learning-rate-free learning by D-Adaptation

Fine-tuning the learning rate (lr) in the training of neural networks is crucial for their performance, and often requires a costly search …

Samuel Burbulla
Optimization in ML
Pill

Physics-informed DeepONets

Physics-informed DeepONets can learn the solution operator of arbitrary partial differential equations, even without any paired …

Samuel Burbulla
Simulation and AI
Pill

Learning nonlinear operators: the DeepONet architecture

The universal approximation theorem for operators suggests a neural network architecture for learning continuous nonlinear operators, called …

Samuel Burbulla
Simulation and AI