The field of physics-informed neural networks (PINNs) and numerical methods is rapidly advancing, with a focus on improving accuracy, efficiency, and applicability to complex problems. Recent developments have led to the creation of new algorithms and techniques, such as the Extended Reference Station Model (ERSM) for magnetic anomaly navigation, and the Trace Regularity Physics-Informed Neural Network (TRPINN) for enforcing boundary conditions. These advancements have the potential to impact various areas, including navigation, optimization, and control. Noteworthy papers include: AMStraMGRAM, which proposes a multi-cutoff adaptation strategy to enhance the performance of ANaGRAM, a natural-gradient-inspired approach for training PINNs. Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features, which introduces an algorithm for iterative training of PINNs with Fourier-enhanced features to overcome the spectral bias issue. NODA-MMH, which experimentally validates the principle of large-scale satellite swarm control through learning-aided magnetic field interactions. These papers demonstrate the innovative and advancing nature of the field, with a focus on developing new methods and techniques to tackle complex problems.
Advancements in Physics-Informed Neural Networks and Numerical Methods
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Extending Temporal Disturbance Estimations For Magnetic Anomaly Navigation and Mapping
Convergence analysis of Sobolev Gradient flows for the rotating Gross-Pitaevskii energy functional
AMStraMGRAM: Adaptive Multi-cutoff Strategy Modification for ANaGRAM
Near-Equilibrium Propagation training in nonlinear wave systems
Trace Regularity PINNs: Enforcing $\mathrm{H}^{\frac{1}{2}}(\partial \Omega)$ for Boundary Data
Numerical Error Analysis of the Poisson Equation under RHS Inaccuracies in Particle-in-Cell Simulations
Trajectory Optimization for Minimum Threat Exposure using Physics-Informed Neural Networks
Convex Maneuver Planning for Spacecraft Collision Avoidance
Energy dissipation and global convergence of a discrete normalized gradient flow for computing ground states of two-component Bose-Einstein condensates
Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features
NODA-MMH: Certified Learning-Aided Nonlinear Control for Magnetically-Actuated Swarm Experiment Toward On-Orbit Proof