Few-Shot Learning by Explicit Physics Integration: An Application to Groundwater Heat Transport

• URL: http://arxiv.org/abs/2507.06062v1
• Date: Tue, 08 Jul 2025 15:06:15 GMT
• Title: Few-Shot Learning by Explicit Physics Integration: An Application to Groundwater Heat Transport
• Authors: Julia Pelzer, Corné Verburg, Alexander Heinlein, Miriam Schulte,
• Abstract summary: Local-Global Convolutional Neural Network (LGCNN) approach is introduced.<n>Model is first systematically analyzed based on random input fields.<n>Then, the model is trained on a handful of cut-outs from a real-world Classical map of the Munich region in Germany.
• Score: 41.94295877935867
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Machine learning methods often struggle with real-world applications in science and engineering due to limited or low-quality training data. In this work, the example of groundwater flow with heat transport is considered; this corresponds to an advection-diffusion process under heterogeneous flow conditions, that is, spatially distributed material parameters and heat sources. Classical numerical simulations are costly and challenging due to high spatio-temporal resolution requirements and large domains. While often computationally more efficient, purely data-driven surrogate models face difficulties, particularly in predicting the advection process, which is highly sensitive to input variations and involves long-range spatial interactions. Therefore, in this work, a Local-Global Convolutional Neural Network (LGCNN) approach is introduced. It combines a lightweight numerical surrogate for the transport process (global) with convolutional neural networks for the groundwater velocity and heat diffusion processes (local). With the LGCNN, a city-wide subsurface temperature field is modeled, involving a heterogeneous groundwater flow field and one hundred groundwater heat pump injection points forming interacting heat plumes over long distances. The model is first systematically analyzed based on random subsurface input fields. Then, the model is trained on a handful of cut-outs from a real-world subsurface map of the Munich region in Germany, and it scales to larger cut-outs without retraining. All datasets, our code, and trained models are published for reproducibility.

Related papers

• A Neural Operator-Based Emulator for Regional Shallow Water Dynamics [5.09419041446345]
  Coastal regions are particularly vulnerable to the impacts of rising sea levels and extreme weather events.<n> Accurate real-time forecasting of hydrodynamic processes in these areas is essential for infrastructure planning and climate adaptation.<n>We present a novel autoregressive neural emulator that employs dimensionality reduction to efficiently approximate high-dimensional numerical solvers.
  arXiv  Detail & Related papers  (2025-02-20T18:02:44Z)
• Learning Pore-scale Multi-phase Flow from Experimental Data with Graph Neural Network [2.2101344151283944]
  Current numerical models are often incapable of accurately capturing the complex pore-scale physics observed in experiments. We propose a graph neural network-based approach and directly learn pore-scale fluid flow using micro-CT experimental data.
  arXiv  Detail & Related papers  (2024-11-21T15:01:17Z)
• Enforcing the Principle of Locality for Physical Simulations with Neural Operators [0.0]
  Time-dependent partial differential equations (PDEs) are strictly local-dependent according to the principle of locality in physics.<n>Deep learning architecture cannot strictly enforce the local-dependency as it inevitably increases the scope of information to make local predictions.<n>This paper proposes a data decomposition method to strictly limit the scope of information for neural operators making local predictions.
  arXiv  Detail & Related papers  (2024-05-02T14:24:56Z)
• Generative Modeling on Manifolds Through Mixture of Riemannian Diffusion Processes [57.396578974401734]
  We introduce a principled framework for building a generative diffusion process on general manifold. Instead of following the denoising approach of previous diffusion models, we construct a diffusion process using a mixture of bridge processes. We develop a geometric understanding of the mixture process, deriving the drift as a weighted mean of tangent directions to the data points.
  arXiv  Detail & Related papers  (2023-10-11T06:04:40Z)
• Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling [16.890326773246414]
  We propose a downscaling method based on the Fourier neural operator. We show that our method significantly outperforms state-of-the-art convolutional and generative adversarial downscaling models. Overall, our work bridges the gap between simulation of a physical process and low-resolution output.
  arXiv  Detail & Related papers  (2023-05-23T18:25:08Z)
• Reduced Order Probabilistic Emulation for Physics-Based Thermosphere Models [0.0]
  This work aims to employ a probabilistic machine learning (ML) method to create an efficient surrogate for the Thermosphere Ionosphere Electrodynamics Circulation General Model (TIE-GCM) We show that across the available data, TIE-GCM ROPE has similar error to previous linear approaches while improving storm-time modeling. We also conduct a satellite propagation study for the significant November 2003 storm which shows that TIE-GCM ROPE can capture the position resulting from TIE-GCM density with 5 km bias.
  arXiv  Detail & Related papers  (2022-11-08T17:36:37Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)
• Learning Large-scale Subsurface Simulations with a Hybrid Graph Network Simulator [57.57321628587564]
  We introduce Hybrid Graph Network Simulator (HGNS) for learning reservoir simulations of 3D subsurface fluid flows. HGNS consists of a subsurface graph neural network (SGNN) to model the evolution of fluid flows, and a 3D-U-Net to model the evolution of pressure. Using an industry-standard subsurface flow dataset (SPE-10) with 1.1 million cells, we demonstrate that HGNS is able to reduce the inference time up to 18 times compared to standard subsurface simulators.
  arXiv  Detail & Related papers  (2022-06-15T17:29:57Z)
• A Gradient-based Deep Neural Network Model for Simulating Multiphase Flow in Porous Media [1.5791732557395552]
  We describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses.
  arXiv  Detail & Related papers  (2021-04-30T02:14:00Z)
• Machine learning for rapid discovery of laminar flow channel wall modifications that enhance heat transfer [56.34005280792013]
  We present a combination of accurate numerical simulations of arbitrary, flat, and non-flat channels and machine learning models predicting drag coefficient and Stanton number. We show that convolutional neural networks (CNN) can accurately predict the target properties at a fraction of the time of numerical simulations.
  arXiv  Detail & Related papers  (2021-01-19T16:14:02Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.