Numerical solutions to the equation for advection are determined using different finite-difference approximations and physics-informed neural networks (PINNs) under conditions that allow an analytical solution. Their accuracy is examined by comparing them to the analytical solution. We used a machine learning framework like PyTorch to implement PINNs. PINNs approach allows training neural networks while respecting the PDEs as a strong constraint in the optimization as apposed to making them part of the loss function. In standard small-scale circulation simulations, it is shown that the conventional approach incorporates a pseudo diffusive effect that is almost as large as the effect of the turbulent diffusion model; hence the numerical solution is rendered inconsistent with the PDEs. This oscillation causes inaccuracy and computational uncertainty. Of all the schemes tested, only the PINNs approximation accurately predicted the outcome. We assume that the PINNs approach can transform the physics simulation area by allowing real-time physics simulation and geometry optimization without costly and time-consuming simulations on large supercomputers.
翻译:平反方程的数值解决方案是在允许分析解决方案的条件下,使用不同的有限差异近似值和物理知情神经网络(PINNs)来确定的,其准确性通过将它们与分析解决方案进行比较来审查。我们使用PyTorrch这样的机器学习框架来实施PINNs。 PINNs 方法允许培训神经网络,同时将PDEs作为优化的强大制约因素,将其作为使其成为损失功能的一部分。在标准的小规模循环模拟中,显示常规方法包含一种与扰动扩散模型效果几乎一样大的假显微效果;因此数字解决方案与PDEs不一致。在所测试的所有计划中,只有PINNs近似值准确预测了结果。我们假设PINNs 方法能够通过允许实时物理模拟和几何测量优化而无需在大型超级计算机上进行昂贵和耗时的模拟来改变物理模拟区域。