In this paper, we empirically demonstrate that natural images can be reconstructed with high fidelity from compressed representations using a simple first-order norm-plus-linear autoregressive (FINOLA) process—without relying on explicit positional information. Through systematic analysis, we observe that the learned coefficient matrices ($\mathbf{A}$ and $\mathbf{B}$) in FINOLA are typically invertible, and their product, $\mathbf{AB}^{-1}$, is diagonalizable across training runs. This structure enables a striking interpretation: FINOLA’s latent dynamics resemble a system of one-way wave equations evolving in a compressed latent space. Under this framework, each image corresponds to a unique solution of these equations. This offers a new perspective on image invariance, suggesting that the underlying structure of images may be governed by simple, invariant dynamic laws. Our findings shed light on a novel avenue for understanding and modeling visual data through the lens of latent-space dynamics and wave propagation.

Full Waveform Inversion (FWI) is a technique used to visualize and analyze wave propagation through a medium in order to infer its physical properties. This method relies on computational models and algorithms to simulate and interpret the behavior of waves—such as sound, electromagnetic, or seismic waves—as they travel through different materials. By analyzing how these waves are reflected, refracted, or absorbed by the medium, FWI can provide detailed information about the medium’s internal structure, composition, and physical properties, such as density, elasticity, or internal defects. The traditional process typically involves: 1) Wave Simulation: Using physics-based models to simulate how waves propagate through a medium. This may involve solving complex differential equations that describe wave behavior in different contexts. 2) Data Acquisition: Collecting data on wave interactions with the medium using sensors or other measurement devices. This could include data on wave speed, direction, amplitude, and phase changes. 3) Image Reconstruction: Applying computational techniques, such as inverse problems or tomographic reconstruction, to create images or maps of the medium based on the acquired wave data. 4) Analysis: Interpreting the reconstructed images to deduce the physical properties of the medium. This can involve identifying features like boundaries, interfaces, or anomalies within the medium.

Subsurface imaging involves solving full waveform inversion (FWI) to predict geophysical properties from measurements. This problem can be reframed as an image-to-image translation, with the usual approach being to train an encoder-decoder network using paired data from two domains: geophysical property and measurement. A recent seminal work (InvLINT) demonstrates there is only a linear mapping between the latent spaces of the two domains, and the decoder requires paired data for training. This paper extends this direction by demonstrating that only linear mapping necessitates paired data, while both the encoder and decoder can be learned from their respective domains through self-supervised learning. This unveils an intriguing phenomenon (named Auto-Linear) where the self-learned features of two separate domains are automatically linearly correlated. Compared with existing methods, our Auto-Linear has four advantages: (a) solving both forward and inverse modeling simultaneously, (b) reducing model size, (c) enhanced performance, especially when the paired data is limited, and (d) strong generalization ability of the trained encoder and decoder.

Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial differential equations (PDEs) like the wave or Maxwell’s equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from measurements to the property directly. In this paper, we show that such a mapping can be well modeled by a very shallow (but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: a near-linear relationship between the input and output, after applying integral transform in high dimensional space. In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer block to reverse the integral of velocity. Experiments show that this interesting property holds for two geophysics inversion problems over four different datasets. Compared to much deeper InversionNet, our method achieves comparable accuracy, but consumes significantly fewer parameters

Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the geophysics community. We present OpenFWI, a collection of large-scale multi-structural benchmark datasets, to facilitate diversified, rigorous, and reproducible research on FWI. In particular, OpenFWI consists of $12$ datasets ($2.1$TB in total) synthesized from multiple sources. It encompasses diverse domains in geophysics (interface, fault, CO$_2$ reservoir, etc.), covers different geological subsurface structures (flat, curve, etc.), and contain various amounts of data samples (2K - 67K). It also includes a dataset for 3D FWI. Moreover, we use OpenFWI to perform benchmarking over four deep learning methods, covering both supervised and unsupervised learning regimes. Along with the benchmarks, we implement additional experiments, including physics-driven methods, complexity analysis, generalization study, uncertainty quantification, and so on, to sharpen our understanding of datasets and methods. The studies either provide valuable insights into the datasets and the performance, or uncover their current limitations. We hope OpenFWI supports prospective research on FWI and inspires future open-source efforts on AI for science. All datasets and related information can be accessed through our website at https://openfwi-lanl.github.io/

Online video sharing (e.g., via YouTube or YouKu) has emerged as one of the most important services in the current Internet, where billions of videos on the cloud are awaiting exploration. Hence, a personalized video retrieval system is needed to help users find interesting videos from big data content. Two of the main challenges are to process the increasing amount of video big data and resolve the accompanying “cold start” issue efficiently. Another challenge is to satisfy the users’ need for personalized retrieval results, of which the accuracy is unknown. In this paper, we formulate the personalized video big data retrieval problem as an interaction between the user and the system via a stochastic process, not just a similarity matching, accuracy (feedback) model of the retrieval; introduce users’ real-time context into the retrieval system; and propose a general framework for this problem. By using a novelcontextualmultiarmed bandit-based algorithm to balance the accuracy and efficiency, we propose a context-based online big-data-oriented personalized video retrieval system. This system can support datasets that are dynamically increasing in size and has the property of cross-modal retrieval. Our approach provides accurate retrieval results withsublinearregret andlinearstorage complexity and significantly improves the learning speed. Furthermore, by learning for a cluster of similar contexts simultaneously, we can realize sublinear storage complexity with the same regret but slightly poorer performance on the “cold start” issue compared to the previous approach. We validate our theoretical results experimentally on a tremendously large dataset; the results demonstrate that the proposed algorithms outperform existing bandit-based online learning methods in terms of accuracy and efficiency and the adaptation from the bandit framework offers additional benefits.