arXiv:2509.23975v2 Announce Type: replace-cross Abstract: The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural
The increasing complexity and computational demands of controlling distributed parameter systems, coupled with advances in neural operator technology, are driving the need for more efficient, data-driven control methods.
This development offers a potential breakthrough for controlling complex, high-dimensional systems in situations where explicit physical models are unavailable or computationally prohibitive, impacting fields from engineering to environmental science.
The reliance on explicit equations for fine-scale simulators in 'equation-free' control is being replaced by data-driven local neural operators, potentially making previously intractable control problems manageable.
- · AI/ML researchers in control theory
- · Industries with complex distributed systems (e.g., aerospace, energy)
- · Data-driven control solution providers
- · Traditional simulation-heavy control design methodologies
- · Developers of purely physics-based control models
More efficient and scalable control of previously unmanageable complex distributed parameter systems will become possible.
This could accelerate the deployment of autonomous systems in environments with variable and high-dimensional dynamics, reducing operational costs and increasing precision.
The reduced dependency on explicit physical models could democratize access to advanced control design, allowing more data-rich, model-poor domains to benefit from sophisticated automation.
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Read at arXiv cs.LG