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DRIFT-Net: A Spectral--Coupled Neural Operator for PDEs Learning

Conference: ICLR2026
arXiv: 2509.24868
Code: None
Area: Scientific Computing
Keywords: neural operator, PDE, spectral coupling, dual-branch, Navier-Stokes

TL;DR

DRIFT-Net is a dual-branch neural operator that addresses autoregressive drift caused by insufficient global spectral coupling in window attention, via controlled low-frequency mixing (spectral branch), local detail fidelity (image branch), and bandwidth fusion through radial gating. It reduces error by 7%–54% on Navier-Stokes benchmarks.

Background & Motivation

State of the Field

Background: Most PDE foundation models employ multi-scale window self-attention, which is computationally efficient but propagates global dependencies only gradually through deep stacking and window shifting.

Limitations of Prior Work: The locality of window attention weakens global spectral coupling, leading to drift in closed-loop rollouts; purely spectral operators (e.g., FNO) over-emphasize low frequencies.

Key Challenge: The inherent trade-off between global coupling and local detail fidelity.

Goal: Enhance global spectral coupling while preserving high-frequency details.

Core Idea: Learnable low-frequency linear mixing + radial gating bandwidth fusion + frequency-weighted loss.

Method

Overall Architecture

A U-Net encoder–decoder in which each scale contains a spectral branch (rFFT2 → low-frequency mixing → bandwidth fusion → iFFT2) and an image branch (ConvNeXt), combined via additive fusion.

Key Designs

  1. Controlled Low-Frequency Mixing: After rFFT2, a learnable complex linear transform is applied exclusively to low-frequency components while high frequencies remain unchanged, preventing interference with fine details.
  2. Bandwidth Fusion + Radial Gating: \(\hat{Y}(k) = \alpha(k)\hat{V}_{low}(k) + (1-\alpha(k))\hat{X}_{high}(k)\); the convex combination guarantees no energy overshoot.
  3. Frequency-Weighted Loss: \(w(r) \propto r^\alpha\) up-weights high-frequency errors to counteract spectral bias.

Loss & Training

Single-step teacher-forcing training; autoregressive closed-loop rollout at test time.

Key Experimental Results

Main Results: 7 PDE Benchmarks

Task scOT FNO DRIFT-Net
NS-SL 3.96% 3.69% 3.40%
NS-PwC 2.35% 4.57% Best
Poisson-Gauss — — Best
Allen-Cahn — — Best
Wave-Gauss — — Best

Efficiency Comparison

Approximately 15% fewer parameters than scOT with higher throughput; NS errors reduced by 7%–54%.

Ablation Study

Configuration Effect
w/o low-frequency mixing Significant error increase
Hard mask instead of radial gating Instability
w/o frequency-weighted loss Insufficient high-frequency fitting
Full DRIFT-Net Best

Key Findings

  • Controlled low-frequency mixing is critical — removing it causes a substantial error increase.
  • Low drift is maintained over 100-step long-horizon rollouts.
  • Effective across elliptic, parabolic, and hyperbolic PDEs.

Highlights & Insights

  • The spectral–spatial dual-branch elegantly decouples global structure from local details, with strong physical intuition.
  • The convex combination in non-expansive fusion ensures training stability.
  • Modular design — the DRIFT block can replace existing attention blocks.

Limitations & Future Work

  • The low-frequency mask size requires manual tuning.
  • Validation is primarily on 2D PDEs; extension to 3D remains untested.
  • Comparison with other PDE foundation models such as DPOT is insufficient.
  • vs. scOT/POSEIDON: Achieves global coupling via the spectral branch without requiring deep stacking.
  • vs. FNO: FNO operates over all frequencies but lacks local capacity; DRIFT-Net's dual branches are complementary.
  • vs. PDE-Refiner: PDE-Refiner relies on iterative refinement, whereas DRIFT-Net achieves fidelity through architectural design.

Rating

  • Novelty: ⭐⭐⭐⭐ An elegant combination of controlled low-frequency mixing, bandwidth fusion, and frequency-weighted loss.
  • Experimental Thoroughness: ⭐⭐⭐⭐⭐ Seven PDE benchmarks, ablations, and long-horizon rollout evaluation.
  • Writing Quality: ⭐⭐⭐⭐ Physical intuition is well articulated.
  • Value: ⭐⭐⭐⭐ Provides a stronger backbone for PDE foundation models.