Advances in Inverse Problems and Geometric Deep Learning

The field of inverse problems and geometric deep learning is rapidly advancing, with a focus on developing innovative methods to tackle complex challenges. Researchers are exploring the intersection of deep learning and geometric techniques to improve the accuracy and efficiency of inverse problem solutions. One notable direction is the incorporation of uncertainty quantification and manifold learning to enhance the robustness and interpretability of predictive models. Another area of interest is the development of novel representation frameworks, such as tensor decomposed multi-resolution grid encoding, to improve the reconstruction of high-dimensional images from low-dimensional compressed measurements. Noteworthy papers include:

  • Learning-Enhanced Variational Regularization for Electrical Impedance Tomography via Calderon's Method, which proposes a deep learning-based method to capture a priori information about the shape and location of unknown contrasts.
  • Leveraging Manifold Embeddings for Enhanced Graph Transformer Representations and Learning, which prepends a lightweight Riemannian mixture-of-experts layer to route each node to various kinds of manifolds, improving graph transformer representations.

Sources

Learning-Enhanced Variational Regularization for Electrical Impedance Tomography via \Calderon's Method

Uncertainty Quantification as a Complementary Latent Health Indicator for Remaining Useful Life Prediction on Turbofan Engines

Estimating Dataset Dimension via Singular Metrics under the Manifold Hypothesis: Application to Inverse Problems

Leveraging Manifold Embeddings for Enhanced Graph Transformer Representations and Learning

Compressive Imaging Reconstruction via Tensor Decomposed Multi-Resolution Grid Encoding

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