Reformulating Neural Operators
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Reformulating Neural Operators in $d+1$ Dimensions for Embedding Evolution
arXiv:2505.11766v4 Announce Type: replace Abstract: Neural Operators (NOs) are powerful architectures for learning mappings between function spaces. While most advances focus on refining kernel parameterizations over the $d$-dimensional physical domain, the evolution of lifted embeddings remains underexplored, which often drives models toward computationally expensive embedding-scaling designs to improve approximation. In this paper, we introduce an auxiliary function dimension that models...
Graph Neural Networks for Fast Operator Selection in Adaptive VQE
arXiv:2606.08794v1 Announce Type: cross Abstract: Adaptive variational quantum algorithms like ADAPT-VQE construct tailored ans\"atze by iteratively selecting operators from a pool using gradient-based criteria. While this avoids oversized parameter spaces, repeatedly scanning the full pool incurs a classical cost that scales linearly with pool size-a major bottleneck for systems with long-range interactions or large operator sets. Here, we reformulate adaptive operator selection as a...
On the Effect of Neural Field Reparameterization for 4DVAR
Announce Type: replace Abstract: Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, yet it remains computationally intensive and sensitive to initialization due to the non-convexity of its objective function. We propose a neural field-based reformulation of 4DVAR in which the spatiotemporal state is represented as a continuous function parameterized by a neural network. We demonstrate that optimizing in parameter space leverages the...
On the Effect of Neural Field Reparameterization for 4DVAR
Announce Type: replace-cross Abstract: Four-dimensional variational data assimilation (4DVAR) is a cornerstone of numerical weather prediction, yet it remains computationally intensive and sensitive to initialization due to the non-convexity of its objective function. We propose a neural field-based reformulation of 4DVAR in which the spatiotemporal state is represented as a continuous function parameterized by a neural network.
Operator learning for solving Fokker-Planck equations with various initial conditions
arXiv:2606.09434v1 Announce Type: new Abstract: The Fokker-Planck equation (FPE) plays a pivotal role in describing the time evolution of probability density functions (PDFs) for systems governed by stochastic dynamics. In this work, we propose a conditional normalizing flow-based physics-informed neural network (PINN) framework for efficiently approximating the solution operator of the FPE for a whole range of initial conditions. Leveraging the Chapman-Kolmogorov equation for Markovian...
Learning to Refine: Spectral-Decoupled Iterative Refinement Framework for Precipitation Nowcasting
arXiv:2606.02661v1 Announce Type: cross Abstract: Accurate precipitation nowcasting is vital for disaster mitigation, but deep learning methods face a key trade-off: regression models produce over-smoothed, spectrally decaying predictions that blur convective details and violate turbulence power laws; diffusion models generate realistic yet unanchored hallucinations lacking physical grounding. We propose Spectral-Decoupled Iterative Refinement (SDIR), a deterministic framework that...
Multigrade Neural Network Approximation
arXiv:2601.16884v3 Announce Type: replace Abstract: We study multigrade deep learning (MGDL) as a principled framework for structured error refinement in deep neural networks. While the approximation power of neural networks is now relatively well understood, training very deep architectures remains challenging due to highly nonconvex and often ill-conditioned optimization landscapes. In contrast, for relatively shallow networks, most notably certain one-hidden-layer ReLU models, training...