Keskeiset käsitteet
Neural operators, such as Fourier Neural Operators (FNO), can learn solution operators for partial differential equations (PDEs) and other function space mappings. However, training these models is computationally intensive, especially for high-resolution problems. This work introduces the first mixed-precision training method for neural operators, which significantly reduces GPU memory usage and improves training throughput without sacrificing accuracy.
Tiivistelmä
The paper introduces a mixed-precision training method for neural operators, which are a powerful data-driven technique for solving partial differential equations (PDEs) and learning mappings between function spaces. Neural operators can handle high-resolution inputs and outputs, but their training is computationally intensive.
The key insights are:
- The discretization error in neural operators is comparable to the precision error from using mixed precision, so there is no need to run the full-precision Fourier transform.
- A simple greedy algorithm is used to optimize the memory-intensive half-precision tensor contractions in the Fourier Neural Operator (FNO) block.
- Numerical instability issues in mixed-precision FNO are addressed by using a tanh pre-activation before the Fourier transform.
The authors demonstrate their mixed-precision training method on three state-of-the-art neural operator architectures (TFNO, GINO, SFNO) across four different datasets. They achieve up to 50% reduction in GPU memory usage and 58% improvement in training throughput, with little or no reduction in accuracy compared to full-precision training.
The authors also provide theoretical approximation bounds, showing that the precision error is asymptotically comparable to the discretization error already present in neural operators. This justifies the use of mixed precision without significant accuracy degradation.
Additionally, the authors propose a precision scheduling technique that transitions from mixed to full precision during training, which achieves better than the baseline full-precision accuracy in zero-shot super-resolution experiments.
Tilastot
The paper reports the following key metrics:
GPU memory consumption reduction of up to 50%
Training throughput improvement of up to 58%
Test L2 error increase of at most 0.28% compared to full-precision training
Lainaukset
"We show that this is not the case; in fact, we prove that reducing the precision in FNO still guarantees a good approximation bound, when done in a targeted manner."
"We formalize this intuition by rigorously characterizing the approximation and precision errors of FNO and bounding these errors for general input functions. We prove that the precision error is asymptotically comparable to the approximation error."
"Across different datasets and GPUs, our method results in up to 58% improvement in training throughput and 50% reduction in GPU memory usage with little or no reduction in accuracy."