Variational quantum algorithms (VQAs) are leading strategies to reachpractical utilities of near-term quantum devices. However, the no-cloningtheorem in quantum mechanics precludes standard backpropagation, leading toprohibitive quantum resource costs when applying VQAs to large-scale tasks. Toaddress this challenge, we reformulate the training dynamics of VQAs as anonlinear partial differential equation and propose a novel protocol thatleverages physics-informed neural networks (PINNs) to model this dynamicalsystem efficiently. Given a small amount of training trajectory data collectedfrom quantum devices, our protocol predicts the parameter updates of VQAs overmultiple iterations on the classical side, dramatically reducing quantumresource costs. Through systematic numerical experiments, we demonstrate thatour method achieves up to a 30x speedup compared to conventional methods andreduces quantum resource costs by as much as 90\% for tasks involving up to 40qubits, including ground state preparation of different quantum systems, whilemaintaining competitive accuracy. Our approach complements existing techniquesaimed at improving the efficiency of VQAs and further strengthens theirpotential for practical applications.