Solving real-world optimization tasks using physics-informed neural computing.

Area of Science:

• Engineering Optimization
• Machine Learning
• Computational Physics

Background:

• Optimization is critical in engineering disciplines like chip design and spacecraft trajectory determination.
• Machine learning methods such as deep reinforcement learning (RL) and genetic algorithms (GA) are increasingly used for these tasks.
• Existing bottom-up approaches like RL and GA face challenges in finding narrow or unstable optimal solutions.

Purpose of the Study:

• To introduce a novel machine learning-based optimization scheme, the physics-informed neural network (PINN).
• To demonstrate PINN's capability to incorporate physical laws into optimization objectives for enhanced performance.
• To showcase PINN's effectiveness in solving diverse optimization problems, including those with challenging solution landscapes.

Main Methods:

• Developed a physics-informed neural network (PINN) framework for optimization.
• Designed an objective function that integrates governing physical laws, operational constraints, and desired goals.
• Applied the PINN to various optimization tasks: pendulum inversion, shortest-time path determination, and spacecraft swingby trajectory calculation.

Main Results:

• PINNs successfully found optimal paths in well-defined systems with reduced exploration compared to RL and GA.
• PINNs demonstrated the ability to identify narrow and unstable optimal solutions, a significant challenge for other methods.
• The top-down search enabled by PINNs proved effective across a range of optimization problems with varying characteristics.

Conclusions:

• Physics-informed neural networks represent a powerful new paradigm for engineering optimization.
• PINNs offer a more efficient and capable approach, particularly for problems requiring the discovery of complex or unstable solutions.
• The PINN framework shows broad applicability across diverse scientific and engineering optimization challenges.