Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems

arXiv:2606.18305 · math.NA, cs.LG, cs.NA · Submitted 2026-06-16 · Read on arXiv

math.NA, cs.LG, cs.NA

Submitted: 2026-06-16

Updated: 2026-09-23

Terminology

• Accuracy — 38× in this paper · explained in 1 episode
• Inverse Problem — 19× in this paper · explained in 2 episodes
• Benchmark — 15× in this paper · explained in 2 episodes
• Generalization — 14× in this paper · explained in 13 episodes
• Starter-Iterator Neural Operator — 14× in this paper
• DeepONet — 12× in this paper · explained in 2 episodes
• Fidelity — 12× in this paper · explained in 2 episodes
• Ground Truth — 8× in this paper
• Iterative Refinement — 8× in this paper · explained in 3 episodes
• Fourier Neural Operator — 7× in this paper
• Latent Space — 6× in this paper · explained in 7 episodes
• Ablation — 5× in this paper · explained in 1 episode
• Robustness — 5× in this paper · explained in 5 episodes
• Interpretability — 4× in this paper · explained in 15 episodes
• Parameter Efficiency — 4× in this paper · explained in 3 episodes
• Ablation Studies — 2× in this paper · explained in 1 episode
• Ablation study — 2× in this paper · explained in 1 episode
• Activation Function — 2× in this paper · explained in 1 episode
• Benchmarking — 2× in this paper · explained in 3 episodes
• Consistency — 2× in this paper · explained in 3 episodes
• Core — 2× in this paper · explained in 2 episodes
• Hilbert Space — 2× in this paper · explained in 2 episodes
• Adam — 1× in this paper · explained in 2 episodes
• Computational overhead — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Convolutional Neural Networks (CNNs) — 1× in this paper · explained in 2 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Deep Residual Channel Attention Network — 1× in this paper
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Distribution Shift — 1× in this paper · explained in 6 episodes
• Fine-Tuning — 1× in this paper · explained in 5 episodes
• Forward modeling — 1× in this paper · explained in 2 episodes
• Initial Data — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• Proper Orthogonal Decomposition — 1× in this paper
• Reconstruction Error — 1× in this paper · explained in 2 episodes
• Regularization — 1× in this paper · explained in 3 episodes
• Representation Learning — 1× in this paper · explained in 2 episodes
• Structural Constraints — 1× in this paper · explained in 2 episodes
• Transfer Learning — 1× in this paper · explained in 10 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• OpenBreastUS: Benchmarking Neural Operators for Wave Imaging Using Breast Ultrasound Computed Tomography
• An overview of condensation phenomenon in deep learning
• Neural Born Series Operator for Biomedical Ultrasound Computed Tomography

Related papers

• Do physics-informed neural networks (PINNs) need to be deep? Shallow PINNs using the Levenberg-Marquardt algorithm
• A Neural-preconditioned Poisson Solver for Mixed Dirichlet and Neumann Boundary Conditions
• Second-order consistency for learning chaotic dynamics via randomized Jacobian matching
• Windowed thinning and query complexity for the bouncy particle and Zigzag samplers
• Data-efficient Kernel Methods for Learning Hamiltonian Systems
• Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems