A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications
arXiv:2606.28519v1 Announce Type: new Abstract: Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints, and limited training data. These challenges arise in many scientific and engineering applications, including subsurface flow, climate modeling, and geological carbon storage (GCS). In this work, we propose a scalable operator-learning framework based on the Karhunen-Loeve Deep Neural Network (KL-DNN) and demonstrate its performance for modeling GCS. The model is trained
The increasing scale and complexity of scientific and engineering problems, coupled with advancements in deep learning, necessitate more efficient and scalable operator learning frameworks.
This development addresses critical bottlenecks in applying AI to large-scale physical simulations, which has significant implications for climate modeling, energy, and material science.
The proposed KL-DNN framework offers a more scalable and memory-efficient approach to operator learning for problems governed by PDEs, overcoming current limitations in computational resources and data.
- · AI researchers in scientific computing
- · Carbon capture and storage companies
- · Climate modeling institutions
- · Energy sector
- · Developers of less scalable operator learning models
- · Traditional high-performance computing methods for PDEs
Improved accuracy and efficiency in simulating large-scale physical phenomena like subsurface flow and geological carbon storage.
Accelerated development and optimization of engineered systems dependent on complex PDE solutions.
Potential for new AI-driven design paradigms in fields currently limited by computational simulation capabilities.
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Read at arXiv cs.LG