Nonintrusive Physics-Preserving Reduced-Order Modeling of Large-Scale Lagrangian Dynamical Systems

Keskeiset käsitteet

The core message of this work is to develop a nonintrusive data-driven method, called Lagrangian operator inference (L-OpInf), that can learn reduced-order models (ROMs) of large-scale Lagrangian dynamical systems while preserving the underlying Lagrangian structure.

Tiivistelmä

The key highlights and insights of this work are:

The authors develop a nonintrusive physics-preserving method called Lagrangian operator inference (L-OpInf) to learn ROMs of large-scale Lagrangian systems, including nonlinear wave equations and mechanical systems with external nonconservative forcing.

The proposed L-OpInf method exploits knowledge about the space-time continuous Lagrangian at the PDE level to define and parametrize a Lagrangian ROM form, which is then learned from trajectory data via a constrained linear least-squares problem.

Numerical results demonstrate that the learned Lagrangian ROMs can accurately predict the physical solutions both far outside the training time interval and for unseen initial conditions, unlike standard operator inference methods that violate the underlying Lagrangian structure.

The authors learn Lagrangian ROMs for a high-dimensional soft-robotic fishtail model with dissipation and time-dependent control input, showcasing the versatility and robustness of the proposed method to unknown control inputs.

Unlike structure-preserving Hamiltonian approaches that require both trajectory and momentum data, the presented L-OpInf method can learn accurate and stable ROMs with bounded energy error from high-dimensional trajectory data alone.

Tilastot

The authors do not provide any specific numerical data or metrics in the content. The focus is on the methodology and numerical demonstrations.

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There are no direct quotes from the content that are relevant to the key logics.

Tärkeimmät oivallukset

Preserving Lagrangian structure in data-driven reduced-order modeling of large-scale dynamical systems

by Harsh Sharma... klo arxiv.org 04-05-2024

https://arxiv.org/pdf/2203.06361.pdf

Syvällisempiä Kysymyksiä

How can the proposed L-OpInf method be extended to learn ROMs that also preserve additional invariants of motion associated with the symmetries of the Lagrangian

The proposed L-OpInf method can be extended to learn ROMs that preserve additional invariants of motion associated with the symmetries of the Lagrangian by incorporating these invariants into the optimization framework. In Lagrangian systems, symmetries of the system Lagrangian correspond to conserved quantities or invariants of motion. By including these additional invariants as constraints in the optimization problem, the learned reduced operators can be tailored to preserve not only the Lagrangian structure but also these symmetries. This extension would involve formulating the optimization problem to minimize the discrepancy between the reduced system dynamics and the invariants of motion, ensuring that the learned ROMs accurately capture these additional conservation laws.

Can the L-OpInf framework be adapted to learn ROMs that preserve the symplectic structure of the original Lagrangian system, in addition to the Lagrangian structure

Yes, the L-OpInf framework can be adapted to learn ROMs that preserve the symplectic structure of the original Lagrangian system in addition to the Lagrangian structure. The symplectic structure in Lagrangian systems is crucial for ensuring the preservation of energy and momentum conservation properties. By incorporating constraints that enforce the preservation of the symplectic structure in the optimization problem, the learned reduced operators can be tailored to maintain the symplectic properties of the system. This adaptation would involve including terms in the optimization objective that ensure the symplecticity of the learned ROMs, thereby guaranteeing the conservation of energy and momentum in the reduced system.

What are the potential applications of the physics-preserving Lagrangian ROMs learned using the L-OpInf method in areas such as real-time simulation, control, and uncertainty quantification of large-scale engineering systems

The physics-preserving Lagrangian ROMs learned using the L-OpInf method have a wide range of potential applications in various engineering domains. In real-time simulation, these ROMs can provide computationally efficient models for simulating the behavior of large-scale dynamical systems with reduced computational cost. In control applications, the learned ROMs can be used to design and implement control strategies for complex systems, enabling precise and efficient control of system dynamics. Additionally, in uncertainty quantification, the Lagrangian ROMs can be utilized to assess the impact of uncertainties on system behavior and make informed decisions in the presence of varying conditions. Overall, the applications of these physics-preserving ROMs span areas such as structural design optimization, real-time simulation, control, and uncertainty quantification in engineering systems.