Simulating mantle convection often requires reaching a computationally expensive steady-state, crucial for deriving scaling laws for thermal and dynamical flow properties and benchmarking numerical solutions. The strong temperature dependence of the rheology of mantle rocks causes viscosity variations of several orders of magnitude, leading to a slow-evolving stagnant lid where heat conduction dominates, overlying a rapidly-evolving and strongly convecting region. Time-stepping methods, while effective for fluids with constant viscosity, are hindered by the Courant criterion, which restricts the time step based on the system's maximum velocity and grid size. Consequently, achieving steady-state requires a large number of time steps due to the disparate time scales governing the stagnant and convecting regions. We present a concept for accelerating mantle convection simulations using machine learning. We generate a dataset of 128 two-dimensional simulations with mixed basal and internal heating, and pressure- and temperature-dependent viscosity. We train a feedforward neural network on 97 simulations to predict steady-state temperature profiles. These can then be used to initialize numerical time stepping methods for different simulation parameters. Compared to typical initializations, the number of time steps required to reach steady-state is reduced by a median factor of 3.75. The benefit of this method lies in requiring very few simulations to train on, providing a solution with no prediction error as we initialize a numerical method, and posing minimal computational overhead at inference time. We demonstrate the effectiveness of our approach and discuss the potential implications for accelerated simulations for advancing mantle convection research.

翻译：模拟地幔对流通常需要达到计算成本高昂的稳态，这对于推导热流与动力学流动特性的标度律以及基准化数值解至关重要。地幔岩石流变学强烈的温度依赖性会导致粘度发生数个数量级的变化，从而形成一个演化缓慢、热传导占主导的停滞盖层，覆盖在一个快速演化且强烈对流的区域之上。时间步进法对于粘度恒定的流体虽然有效，但受限于Courant准则，该准则基于系统的最大速度和网格尺寸来限制时间步长。因此，由于停滞区与对流区所遵循的时间尺度差异巨大，达到稳态需要大量的时间步。我们提出了一种利用机器学习加速地幔对流模拟的概念。我们生成了一个包含128个二维模拟的数据集，这些模拟具有混合的基底加热与内部加热，以及压力与温度依赖的粘度。我们在97个模拟上训练了一个前馈神经网络，以预测稳态温度剖面。这些剖面随后可用于为不同的模拟参数初始化数值时间步进法。与典型的初始化方法相比，达到稳态所需的时间步数中位数减少了3.75倍。该方法的好处在于仅需极少量的模拟进行训练，通过初始化数值方法提供无预测误差的解，并且在推理时产生的计算开销极小。我们证明了该方法的有效性，并讨论了加速模拟对推进地幔对流研究的潜在意义。