Proven theoretically for linear PDEs, validated experimentally on nonlinear ones like Burgers' equation. Time to rethink data-driven ML benchmarks for higher physical fidelity!

We show neural emulators trained on low-fidelity data can outperform their source simulators—thanks to inductive biases and smarter error accumulation—beating them against high-fidelity references.

Can your AI surpass the simulator that taught it? What if the key to more accurate PDE modeling lies in questioning your training data's origins? 🤔

Excited to share my #NeurIPS 2025 paper with @thuereygroup.bsky.social: "Neural Emulator Superiority"!

Art.

And to enforce good practices APEBench is designed around controllable deterministic pseudo-randomness that allows for straightforward run of seed statistics that can be used to perform hypothesis tests.

Another important contribution is that APEBench defines most of its PDEs via a new parameterization that we call "difficulties". Those allow for expressing a wide range of different dynamics with a reduced and interpretable set of numbers.

This allows for investigating how unrolled training helps with long-term accuracy.

Temporal Axis also means various configurations of how emulator and simulator interact during training, for example, in terms of supervised unrolled training. We generalize many approaches seen in the literature in terms of unrolled steps T and branch steps B.

One core motivation for APEBench was the temporal axis in emulator learning (hence the "autoregressive" in APE). We focus on rollout metrics and sample rollouts to truly understand temporal generalization via long-term stability and accuracy in more than 20 metrics.

This numerical solver is based on Fourier-pseudo spectral ETDRK methods, one of the most efficient numerical techniques to solve semi-linear PDEs on periodic boundaries for which we provide a wide range of pre-defined configurations (46 as of the initial release).

With it, we can _procedurally_ generate all data ever needed in seconds on a modern GPU --- yes, this means you do not have to download hundreds of GBs of data. Installing the APEBench Python package (<1MB) is sufficient. 😎

The key innovation is to tightly integrate a classical numerical solver that produces all the synthetic training data with incredible efficiency and allows for easy scenario customization.

Happy new year! 🎉 Two days ago we entered 2025 and just in time the channel surpassed 25k subscribers. Wow! Thanks to everyone for their kind words and support along the way: www.youtube.com/channel/UCh0...

Now presenting APEBench at #NeurIPS in West #5407.

I will be presenting my poster on APEBench on Thursday from 11:00 to 14:00 PST at West Ballroom A-D #5407.

This was done as part of my PhD with @thuereygroup.bsky.social in collaboration with my talented co-author, Simon Niedermayr, who is supervised by Rüdiger Westermann.