Implicit Formulation

Implicit formulation is a growing area of research focusing on representing and solving problems indirectly, often by defining relationships implicitly rather than explicitly. Current research explores this approach across diverse fields, including optimization, robotics, and machine learning, employing techniques like neural networks, kernel methods, and novel numerical integration schemes tailored to specific problem structures (e.g., Lie groups for multibody systems). This shift towards implicit methods offers advantages in stability, robustness, and computational efficiency for handling complex, high-dimensional systems, particularly those involving discontinuities or constraints, leading to improved performance in applications ranging from physical simulation to automated problem solving.