Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural network and data, often fail to accurately simulate the evolution of the system dynamics over a sufficiently long time and in a physically consistent manner. Therefore, we propose a hybrid approach that uses a neural network model in combination with an incomplete partial differential equations (PDEs) solver that provides known, but incomplete physical information. In this study, we demonstrate that the results obtained from the incomplete PDEs can be efficiently corrected at every time step by the proposed hybrid neural network—PDE solver model, so that the effect of the unknown physics present in the system is correctly accounted for. For validation purposes, the obtained simulations of the hybrid model are successfully compared against results coming from the complete set of PDEs describing the full physics of the considered system. We demonstrate the validity of the proposed approach on a reactive flow, an archetypal multi-physics system that combines fluid mechanics and chemistry, the latter being the physics considered unknown. Experiments are made on planar and Bunsen-type flames at various operating conditions. The hybrid neural network—PDE approach correctly models the flame evolution of the cases under study for significantly long time windows, yields improved generalization and allows for larger simulation time steps.

The present study explores whether embodied meaning is activated in comprehension of action-related Mandarin counterfactual sentences. Participants listened to action-related Mandarin factual or counterfactual sentences describing transfer events (actions towards or away from the participant), and then performed verb-compatible or -incompatible motor action after a transfer verb (action towards or away from the participant) onset. The results demonstrated that motor simulation, specifically the interfering action-sentence compatibility effect (ACE), was obtained in both factual and counterfactual sentences. Additionally, the temporal course of motor resonance was slightly different between factual and counterfactual sentences. We concluded that embodied meaning was activated in action-related Chinese counterfactual sentences. The results supported a neural network model of Chersi, Thill, Ziemke, and Borghi (2010), proposed within the embodiment approach, which explains the interaction between processing action-related sentences and motor performance. Moreover, we speculated that the neural network model of Chersi et al. was also applicable to action-related Mandarin counterfactual comprehension.

Research on new techniques of perforated silencers has been well addressed. However, the research work on shape optimization for a volume-constrained silencer within a constrained machine room is rare. Therefore, the optimum design of mufflers becomes an essential issue. In this paper, to simplify the optimum process, a simplified mathematical model of the muffler is constructed with a neural network using a series of input design data (muffle dimensions) and output data (theoretical sound transmission loss) obtained by a theoretical mathematical model (TMM). To assess the optimal mufflers, the neural network model (NNM) is used as an objective function in conjunction with a genetic algorithm (GA). Moreover, the numerical cases of sound elimination with respect to pure tones (500, 1000, 2000Hz) are exemplified and discussed.

Before the GA operation can be carried out, the accuracy of the TMM is checked by Crocker's experimental data. In addition, both the TMM and NNM are compared. It is found that the TMM and the experimental data are in agreement. Moreover, the TMM and NNM confirm.

The results reveal that the maximum value of the sound transmission loss (STL) can be optimally obtained at the desired frequencies. Consequently, it is obvious that the optimum algorithm proposed in this study can provide an efficient way to develop optimal silencers.