# When Do PINNs Beat Classical Numerical Methods? A 1D vs 5D Experiment

DevFeed: [When Do PINNs Beat Classical Numerical Methods? A 1D vs 5D Experiment](<https://devfeed.tech/articles/when-do-pinns-beat-classical-numerical-methods-a-1d-vs-5d-experiment-66769.md>)

Original publisher: [Read original article](<https://towardsdatascience.com/when-do-pinns-beat-classical-numerical-methods-a-1d-vs-5d-experiment/>)

Author: Samit Ganguly

Published: 2026-10-07T11:00:00Z

Content type: article

Language: en

Sources: [Towards Data Science](<https://devfeed.tech/sources/towards-data-science.md>)

Topics: [Artificial Intelligence](<https://devfeed.tech/topics/ai.md>), [Physics-guided deep learning](<https://devfeed.tech/topics/physics-guided-deep-learning.md>), [Computational Fluid Dynamics (CFD)](<https://devfeed.tech/topics/cfd.md>)

Tags: [curse-of-dimensionality](<https://devfeed.tech/tags/curse-of-dimensionality.md>), [data](<https://devfeed.tech/tags/data.md>), [data-science](<https://devfeed.tech/tags/data-science.md>), [deep-learning](<https://devfeed.tech/tags/deep-learning.md>), [machine-learning](<https://devfeed.tech/tags/machine-learning.md>), [neural-network](<https://devfeed.tech/tags/neural-network.md>), [numerical-methods](<https://devfeed.tech/tags/numerical-methods.md>), [physics](<https://devfeed.tech/tags/physics.md>), [physics-informed](<https://devfeed.tech/tags/physics-informed.md>), [pytorch](<https://devfeed.tech/tags/pytorch.md>), [science](<https://devfeed.tech/tags/science.md>)

## AI overview

The article compares physics-informed neural networks (PINNs) with finite-difference methods for a quantum harmonic oscillator in one and five dimensions. Finite differences are much faster in 1D, while a PINN reaches about 0.1% error in 5D where a generic grid would require roughly five billion points and more than a terabyte of memory. The author cautions that the 5D problem is separable, so classical methods using that structure could solve it efficiently; the comparison does not show PINNs outperforming every classical method.

## Source excerpt

I put a physics-informed neural network up against a plain finite-difference solver twice: once in 1D and once in 5D. The winner changed. The post When Do PINNs Beat Classical Numerical Methods? A 1D vs 5D Experiment appeared first on Towards Data Science.