arXiv:2606.07601v1 Announce Type: new Abstract: We introduce the Laplace-Fourier Neural Operator (LFNO), a unified framework for modeling dynamical systems across transient and steady-state regimes by integrating the spectral advantages of Laplace and Fourier Neural Operators. LFNO employs a dual-branch architecture that explicitly decomposes system dynamics into transient and steady-state components. We evaluate LFNO on nine benchmarks, including three ODE systems (Duffing, Lorenz, and Pendulum) and six PDE systems (Euler-Bernoulli beam, Heat, Reaction-diffusion, Brusselator, Burgers, and Nav
This development emerges as the field of AI seeks more robust and generalizable methods for modeling complex physical systems, moving beyond task-specific models.
A unified framework like LFNO could significantly improve the predictability and efficiency of AI models in scientific and engineering applications, accelerating discovery and design cycles.
The ability to seamlessly model both transient and steady-state dynamics in complex systems within a single AI framework reduces the need for specialized algorithms and improves overall simulation accuracy.
- · AI researchers
- · Engineering simulation software
- · Materials science
- · Climate modeling
- · Traditional numerical solvers
- · Specialized domain-specific modeling software without AI integration
LFNO improves the accuracy and efficiency of AI-driven simulations for phenomena like fluid dynamics, weather patterns, and structural integrity.
Faster and more accurate simulations could accelerate R&D across various industries, from aerospace to pharmaceuticals, by enabling rapid prototyping and predictive maintenance.
This could lead to a new generation of AI-designed materials or structures with unprecedented properties, fundamentally altering manufacturing and industrial capabilities.
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Read at arXiv cs.LG