Variational quantum algorithms (VQAs) are leading strategies to reach<br>practical utilities of near-term quantum devices. However, the no-cloning<br>theorem in quantum mechanics precludes standard backpropagation, leading to<br>prohibitive quantum resource costs when applying VQAs to large-scale tasks. To<br>address this challenge, we reformulate the training dynamics of VQAs as a<br>nonlinear partial differential equation and propose a novel protocol that<br>leverages physics-informed neural networks (PINNs) to model this dynamical<br>system efficiently. Given a small amount of training trajectory data collected<br>from quantum devices, our protocol predicts the parameter updates of VQAs over<br>multiple iterations on the classical side, dramatically reducing quantum<br>resource costs. Through systematic numerical experiments, we demonstrate that<br>our method achieves up to a 30x speedup compared to conventional methods and<br>reduces quantum resource costs by as much as 90\% for tasks involving up to 40<br>qubits, including ground state preparation of different quantum systems, while<br>maintaining competitive accuracy. Our approach complements existing techniques<br>aimed at improving the efficiency of VQAs and further strengthens their<br>potential for practical applications.