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In this paper, we propose a new deep learning method for the nonlinear Poisson-Boltzmann problems with applications in computational biology. To tackle the discontinuity of the solution, e.g., across protein surfaces, we approximate the solution by a piecewise mesh-free neural network that can capture the dramatic change in the solution across the interface. The partial differential equation problem is first reformulated as a least-squares physics-informed neural network (PINN)-type problem and then discretized to an objective function using mean squared error via sampling. The solution is obtained by minimizing the designed objective function via standard training algorithms such as the stochastic gradient descent method. Finally, the effectiveness and efficiency of the neural network are validated using complex protein interfaces on various manufactured functions with different frequencies.
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