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TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion

TANTE is a new operator-learning framework for time-dependent PDEs that uses neural Taylor expansion to make accurate, continuous-time predictions with adaptive step sizes, improving both accuracy and efficiency over fixed-step methods.

This repository contains code accompanying the paper titled TANTE: Time-Adaptive Operator Learning via Neural Taylor Expansion.

🧱 Pipeline

Time-Adaptive Transformer with Neural Taylor Expansion (TANTE). Our framework enables continuous-time prediction with dynamically adjusted step sizes based on local temporal complexity. TANTE generates forecasts by summing the predicted derivatives as a Taylor series within the confidence interval.

📦 Installation

cd TANTE

# (Optional) create conda env
conda create -n tante python=3.11
conda activate tante

pip install -r requirements.txt

📚 Datasets

Our data is from The Well datasets — Turbulent Radiative Layer, Active Matter, Viscoelastic Instability, Rayleigh–Bénard — collected by PolymathicAI. Follow their repo to download raw files, then organise them as:

datasets/
└─ active_matter/
   ├─ active_matter.yaml
   ├─ stats.yaml
   └─ data/
      ├─ train/   *.hdf5
      ├─ valid/   *.hdf5
      └─ test/    *.hdf5

Then set root_path in configs/<model>.yaml accordingly.

🚀 Training

# Train from scratch / Resume (same <experiment> name)
python train.py --config-name=<model_name>

Logs → output/, Checkpoints → experiments/<experiment>/.

Our repository also provides a PyTorch implementation of Continuous Vision Transformer (CViT), adapted from its original JAX codebase to broaden accessibility and adoption.

🔎 Evaluation

python eval.py --config-name=<model_name>

eval.py auto-loads the checkpoint specified by experiment in the config of <model_name>.

🏆 Main Results

Representative TANTE rollout predictions across four benchmarks. Each benchmark's results are shown in three rows: the first row displays the ground truth field (reference), the second row shows the predictions from TANTE, and the third row illustrates the point-wise absolute error between the predictions and the ground truth. Left: $Buoyancy$ field in the Rayleigh-Bénard convection (RB) benchmark across eight time steps. Top Right $Velocity$ field (y-direction) in the Active Matter (AM) benchmark across sixteen time steps. Middle Right: $C_{xx}$ field in the Viscoelastic Instability fluids (VF) benchmark across sixteen time steps. Bottom Right: $Density$ field in the Turbulent Radiative Layer (TR) benchmark across fourteen time steps.

Predictions of the target field at $t=4$ time step on the four benchmarks. For each dataset, we show one representative sample comparing our approach with the best performance against several competitive baselines with top accuracy.