Self-adaptive neural tangent Kernel-weighted physics-informed neural network for radiative MHD mixed convection in reactive nanofluid slip flow over a moving vertical plate

Reliable prediction of heat and mass transfer in magnetized nanofluids is central to the design of solar collectors, electronic cooling systems, and microfluidic devices, yet the governing equations for such flows are strongly nonlinear and traditionally require mesh-based numerical solvers that are costly to re-run for every new set of operating conditions. This work develops a mesh-free deep-learning solver for the boundary-layer flow of a chemically reactive, radiating, magnetically influenced nanofluid moving past a vertical plate with slip at the wall, where velocity, temperature, and particle concentration are all allowed to depart from the plate value. The central methodological advance is a training scheme in which the relative emphasis placed on the momentum, energy, concentration, and boundary-condition constraints is adjusted automatically during learning, using a measure of how quickly each constraint is being satisfied by the network; this is combined with a sampling strategy that concentrates training effort in the thin near-wall region where gradients are steepest. Compared with a fixed-weight version of the same network, the adaptive scheme lowers the mean-squared solution error from the 1 0 − 5 – 1 0 − 4 range to the 1 0 − 8 – 1 0 − 6 range, a reduction of one to two orders of magnitude, while also training about 2.5 times faster and matching finite-element benchmark values to within roughly 1%. Across the parameter ranges studied, stronger magnetic fields are found to slow the flow and raise the temperature, stronger radiation and internal heating broaden the thermal layer and lower the surface heat-transfer rate, and a faster chemical reaction thins the concentration layer and raises the surface mass-transfer rate; wall slip weakens all three transport rates simultaneously. Because the trained network evaluates new parameter combinations in a fraction of a second, it also functions as a fast surrogate for parametric and sensitivity studies that would otherwise require many repeated finite-element runs. These results indicate that automatically balancing competing physical constraints during training, rather than fixing their relative weights in advance, is an effective and broadly applicable way to improve the accuracy and reliability of physics-based neural-network solvers for multi-physics transport problems.

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