Track papers across labs, topics, and trends.
Search papers, labs, and topics across Lattice.
This paper introduces Derivative-Constrained Physics-Informed Neural Networks (DC-PINNs), a framework that incorporates general nonlinear constraints on states and derivatives into the PINN loss function. DC-PINNs use automatic differentiation to efficiently compute these constraints and employ self-adaptive loss balancing to minimize manual hyperparameter tuning. Experiments on heat diffusion, financial volatility, and fluid flow benchmarks demonstrate that DC-PINNs reduce constraint violations and improve physical fidelity compared to standard PINNs.
Guaranteeing physically plausible solutions to PDEs just got easier: DC-PINNs leverage derivative constraints and adaptive loss balancing to improve the accuracy and stability of PINN solutions.
Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as fundamental as the governing equations. In this paper, we present Derivative-Constrained PINNs (DC-PINNs), a general framework that treats constrained PDE solving as an optimisation guided by a minimum objective function criterion where the physics resides in the minimum principle. DC-PINNs embed general nonlinear constraints on states and derivatives, e.g., bounds, monotonicity, convexity, incompressibility, computed efficiently via automatic differentiation, and they employ self-adaptive loss balancing to tune the influence of each objective, reducing reliance on manual hyperparameters and problem-specific architectures. DC-PINNs consistently reduce constraint violations and improve physical fidelity versus baseline PINN variants, representative hard-constraint formulations on benchmarks, including heat diffusion with bounds, financial volatilities with arbitrage-free, and fluid flow with vortices shed. Explicitly encoding derivative constraints stabilises training and steers optimisation toward physically admissible minima even when the PDE residual alone is small, providing reliable solutions of constrained PDEs grounded in energy minimum principles.