jNO: A JAX Library for Neural Operator and Foundation Model Training

Leon Armbruster; Rathan Ramesh; Georg Kruse; Christopher Straub

cs.LGMay 11, 2026

jNO: A JAX Library for Neural Operator and Foundation Model Training

Authors: Leon Armbruster, Rathan Ramesh, Georg Kruse, Christopher Straub

Organizations: Fraunhofer Institute for Integrated Systems and Device Technology IISB, Germany

Abstract

jNO (jax Neural Operators) is a JAX-native library for neural operators and foundation models with unified support for both data-driven and physics-informed training. Its core design is a tracing system in which domains, model calls, residuals, supervised losses, and diagnostics are written in one symbolic language and compiled into one optimization pipeline. This allows users to move between operator regression, mesh-aware residual evaluation, and PDE-constrained training without restructuring the surrounding code. jNO also supports multi-model compositions, fine-grained control at parameter level (model, optimizer, and learning rate), hyperparameter tuning, and JAX-native workflows for translated PDE foundation-model families. The source repository is available at https://github.com/FhG-IISB/jNO.

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May 8, 2026 · cs.LGJ/K move · Enter open · S save

Neural Operators as Efficient Function Interpolators

Vasilis Niarchos, Angelos Sirbu, Sokratis Trifinopoulos

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator acting by composition on functions of the base-space. Through a range of benchmarks on analytic functions of increasing complexity and dimensionality, we demonstrate that NOs can match or outperform standard multilayer perceptrons and Kolmogorov--Arnold Networks in accuracy while requiring significantly fewer parameters and training time. As a real-world application, we apply a two-dimensional Tensorized Fourier Neural Operator (TFNO) to the nuclear chart, learning a correction to state-of-the-art nuclear mass models as a partially observed residual field. A TFNO ensemble reaches a held-out root-mean-square error of 198.2 keV, placing it among the best recent neural-network approaches while retaining high parameter efficiency and short training times. More broadly, these results introduce NOs as a scalable framework for finite-dimensional function interpolation, from analytic benchmarks to structured scientific data.

Fourier Neural Operators Neural Operators Nuclear Data Kolmogorov-Arnold Networks Interpolation

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Abstract

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