# SLE-FNO: Single-Layer Extensions for Task-Agnostic Continual Learning in Fourier Neural Operators

arXiv: https://arxiv.org/abs/2603.20410 · HTML: https://mlsanity.com/paper/2603.20410/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 63 of its 143 references that are in the map.
- First posted on arXiv 20 Mar 2026.

## Builds on (most cited first, 30 of 63)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [WILDS: A Benchmark of in-the-Wild Distribution Shifts](https://mlsanity.com/paper/2012.07421/) (2020)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks](https://mlsanity.com/paper/1706.02690/) (2017)
- [Energy-based Out-of-distribution Detection](https://mlsanity.com/paper/2010.03759/) (2020)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [Continual Learning with Deep Generative Replay](https://mlsanity.com/paper/1705.08690/) (2017)
- [Experience Replay for Continual Learning](https://mlsanity.com/paper/1811.11682/) (2018)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [A Comprehensive Survey of Continual Learning: Theory, Method and Application](https://mlsanity.com/paper/2302.00487/) (2023)
- [Generalized Out-of-Distribution Detection: A Survey](https://mlsanity.com/paper/2110.11334/) (2021)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [An Empirical Investigation of Catastrophic Forgetting in Gradient-Based Neural Networks](https://mlsanity.com/paper/1312.6211/) (2013)
- [Overcoming catastrophic forgetting with hard attention to the task](https://mlsanity.com/paper/1801.01423/) (2018)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Three scenarios for continual learning](https://mlsanity.com/paper/1904.07734/) (2019)
- [Online Continual Learning with Maximally Interfered Retrieval](https://mlsanity.com/paper/1908.04742/) (2019)
- [Expert Gate: Lifelong Learning with a Network of Experts](https://mlsanity.com/paper/1611.06194/) (2016)

## Built on by (most cited first, 3 of 3)

- [Replay-Based Continual Learning for Physics-Informed Neural Operators](https://mlsanity.com/paper/2605.04832/) (2026)
- [Wall Shear Stress Reconstruction from Concentration: Differentiable Physics and Physics-Informed Neural Networks](https://mlsanity.com/paper/2606.06313/) (2026)
- [Strategic Governance of AI Models in Earth Science](https://mlsanity.com/paper/2610.10560/) (2026)

## Abstract (arXiv)

Scientific machine learning is increasingly used to build surrogate models, yet most models are trained under a restrictive assumption in which future data follow the same distribution as the training set. In practice, new experimental conditions or simulation regimes may differ significantly, requiring extrapolation and model updates without re-access to prior data. This creates a need for continual learning (CL) frameworks that can adapt to distribution shifts while preventing catastrophic forgetting. Such challenges are pronounced in fluid dynamics, where changes in geometry, boundary conditions, or flow regimes induce non-trivial changes to the solution. Here, we introduce a new architecture-based approach (SLE-FNO) combining a Single-Layer Extension (SLE) with the Fourier Neural Operator (FNO) to support efficient CL. SLE-FNO was compared with a range of established CL methods, including Elastic Weight Consolidation (EWC), Learning without Forgetting (LwF), replay-based approaches, Orthogonal Gradient Descent (OGD), Gradient Episodic Memory (GEM), PiggyBack, and Low-Rank Adaptation (LoRA), within a spatial field-to-field regression setting. The models were trained to map transient concentration fields to time-averaged wall shear stress (TAWSS) in pulsatile aneurysmal blood flow. Tasks were derived from 230 computational fluid dynamics simulations grouped into four sequential and out-of-distribution configurations. Results show that replay-based methods and architecture-based approaches (PiggyBack, LoRA, and SLE-FNO) achieve the best retention, with SLE-FNO providing the strongest overall balance between plasticity and stability, achieving accuracy with zero forgetting and minimal additional parameters. Our findings highlight key differences between CL algorithms and introduce SLE-FNO as a promising strategy for adapting baseline models when extrapolation is required.