Knowing the thermo-mechanical history of a part during its processing is essential to master the final properties of the product. During forming processes, several parameters can affect it. The development of a surrogate model makes it possible to access history in real time without having to resort to a numerical simulation. We restrict ourselves in this study to the cooling phase of the casting process. The thermal problem has been formulated taking into account the metal as well as the mould. Physical constants such as latent heat, conductivities and heat transfer coefficients has been kept constant. The problem has been parametrized by the coolant temperatures in five different cooling channels. To establish the offline model, multiple simulations are performed based on well-chosen combinations of parameters. The space-time solution of the thermal problem has been solved parametrically. In this work we propose a strategy based on the solution decomposition in space, time, and parameter modes. By applying a machine learning strategy, one should be able to produce modes of the parametric space for new sets of parameters. The machine learning strategy uses either random forest or polynomial fitting regressors. The reconstruction of the thermal solution can then be done using those modes obtained from the parametric space, with the same spatial and temporal basis previously established. This rationale is further extended to establish a model for the ignored part of the physics, in order to describe experimental measures. We present a strategy that makes it possible to calculate this ignorance using the same spatio-temporal basis obtained during the implementation of the numerical model, enabling the efficient construction of processing hybrid twins.

了解零件在加工过程中的热机械历史对于掌握产品的最终性能至关重要。在成型过程中，有几个参数会对其产生影响。代理模型的开发使得实时访问历史成为可能，而无需诉诸数值模拟。我们在这项研究中将自己限制在铸造过程的冷却阶段。热问题的制定考虑了金属和模具。潜热、电导率和传热系数等物理常数保持恒定。该问题已通过五个不同冷却通道中的冷却剂温度进行参数化。为了建立离线模型，根据精心选择的参数组合进行多次模拟。热问题的时空解已得到参数化求解。在这项工作中，我们提出了一种基于空间、时间和参数模式的解分解的策略。通过应用机器学习策略，人们应该能够为新的参数集生成参数空间的模式。机器学习策略使用随机森林或多项式拟合回归器。然后可以使用从参数空间获得的那些模式以及先前建立的相同空间和时间基础来完成热解的重建。这一基本原理被进一步扩展，为物理学中被忽略的部分建立了一个模型，以描述实验测量。我们提出了一种策略，可以使用在实施数值模型期间获得的相同时空基础来计算这种无知，从而能够有效地构建处理混合孪生。