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Bogdan Raonic

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3 papers

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NeurIPS Conference 2025 Conference Paper

RIGNO: A Graph-based Framework For Robust And Accurate Operator Learning For PDEs On Arbitrary Domains

Sepehr Mousavi
Shizheng Wen
Levi Lingsch
Maximilian Herde
Bogdan Raonic
Siddhartha Mishra

Learning the solution operators of PDEs on arbitrary domains is challenging due to the diversity of possible domain shapes, in addition to the often intricate underlying physics. We propose an end-to-end graph neural network (GNN) based neural operator to learn PDE solution operators from data on point clouds in arbitrary domains. Our multi-scale model maps data between input/output point clouds by passing it through a downsampled regional mesh. The approach includes novel elements aimed at ensuring spatio-temporal resolution invariance. Our model, termed RIGNO, is tested on a challenging suite of benchmarks composed of various time-dependent and steady PDEs defined on a diverse set of domains. We demonstrate that RIGNO is significantly more accurate than neural operator baselines and robustly generalizes to unseen resolutions both in space and in time. Our code is publicly available at github. com/camlab-ethz/rigno.

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NeurIPS Conference 2023 Conference Paper

Convolutional Neural Operators for robust and accurate learning of PDEs

Bogdan Raonic
Roberto Molinaro
Tim De Ryck
Tobias Rohner
Francesca Bartolucci
Rima Alaifari
Siddhartha Mishra
Emmanuel de Bézenac

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. The resulting architecture, termed as convolutional neural operators (CNOs), is designed specifically to preserve its underlying continuous nature, even when implemented in a discretized form on a computer. We prove a universality theorem to show that CNOs can approximate operators arising in PDEs to desired accuracy. CNOs are tested on a novel suite of benchmarks, encompassing a diverse set of PDEs with multi-scale solutions and are observed to significantly outperform baselines, paving the way for an alternative framework for robust and accurate operator learning.

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NeurIPS Conference 2023 Conference Paper

Representation Equivalent Neural Operators: a Framework for Alias-free Operator Learning

Francesca Bartolucci
Emmanuel de Bézenac
Bogdan Raonic
Roberto Molinaro
Siddhartha Mishra
Rima Alaifari

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators necessitate discretization in the transition to computer implementations. This step can compromise their integrity, often causing them to deviate from the underlying operators. This research offers a fresh take on neural operators with a framework Representation equivalent Neural Operators (ReNO) designed to address these issues. At its core is the concept of operator aliasing, which measures inconsistency between neural operators and their discrete representations. We explore this for widely-used operator learning techniques. Our findings detail how aliasing introduces errors when handling different discretizations and grids and loss of crucial continuous structures. More generally, this framework not only sheds light on existing challenges but, given its constructive and broad nature, also potentially offers tools for developing new neural operators.

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