Path Dependent

Path dependency describes systems where the future state depends not only on the current state but also on the entire history of its evolution. Current research focuses on developing accurate and efficient models for path-dependent phenomena, employing techniques like recurrent neural networks (RNNs), particularly LSTMs, and physics-informed neural networks (PINNs), to capture complex temporal dynamics in diverse applications. These models are being applied to problems ranging from material science (modeling plasticity and damage) and financial modeling (pricing path-dependent derivatives) to robotics (motion planning) and imaging (non-line-of-sight imaging). The ability to accurately model path-dependent systems has significant implications for improving predictions and control across various scientific and engineering disciplines.