FieldFormer: Self-supervised Reconstruction of Physical Fields via Tensor Attention Prior

TL;DR

FieldFormer is a self-supervised neural method that reconstructs physical field tensors from limited, noisy observations using tensor Tucker models and attention mechanisms, avoiding offline training and improving accuracy.

Contribution

The paper introduces FieldFormer, a self-supervised framework that leverages tensor Tucker models and attention to adaptively reconstruct physical fields without offline training.

Findings

Outperforms state-of-the-art baselines in various physical field reconstructions.

Provides theoretical guarantees for recoverability.

Demonstrates flexibility in representing different types of physical fields.

Abstract

Reconstructing physical field tensors from \textit{in situ} observations, such as radio maps and ocean sound speed fields, is crucial for enabling environment-aware decision making in various applications, e.g., wireless communications and underwater acoustics. Field data reconstruction is often challenging, due to the limited and noisy nature of the observations, necessitating the incorporation of prior information to aid the reconstruction process. Deep neural network-based data-driven structural constraints (e.g., ``deeply learned priors'') have showed promising performance. However, this family of techniques faces challenges such as model mismatches between training and testing phases. This work introduces FieldFormer, a self-supervised neural prior learned solely from the limited {\it in situ} observations without the need of offline training. Specifically, the proposed framework starts with modeling the fields of interest using the tensor Tucker model of a high multilinear rank, which ensures a universal approximation property for all fields. In the sequel, an attention mechanism is incorporated to learn the sparsity pattern that underlies the core tensor in order to reduce the solution space. In this way, a ``complexity-adaptive'' neural representation, grounded in the Tucker decomposition, is obtained that can flexibly represent various types of fields. A theoretical analysis is provided to support the recoverability of the proposed design. Moreover, extensive experiments, using various physical field tensors, demonstrate the superiority of the proposed approach compared to state-of-the-art baselines.