深度能量法(Deep Energy Method, DEM)是一種新穎的數值模擬方法，通過結合深度學習和傳統的能量法，能夠更加準確地解決複雜的物理問題。深度能量法通常使用類深度神經網絡進行建模，利用前向傳播和反向傳播算法進行訓練，並在人工神經網絡的幫助下最小化勢能。與傳統的數值方法相比，深度能量法具有許多優勢，例如能夠自適應地學習複雜的物理現象、快速收斂、節省計算成本等，深度能量法還可以通過對神經網絡架構和訓練算法的改進，進一步提高模擬的精度和效率。
許多工程存在能量泛函的問題，深度能量法是一種非常靈活和高效的方法，因為它只需要定義能量函數即可進行分析，而不需要對統御方程式進行求解。此外，標準優化器能夠通過迭代來尋找最小值，而不需要對問題進行繁瑣的手動調整。這種方法通過使用前向傳播的過程來進行無約束逼近，可以快速地進行數值分析，並且受到邊界條件的約束以形成最終預測。
透過求解壓電材料梁及熱彈性體等耦合問題，驗證了本法的有效性，提供了一種新的數值分析方法。

The Deep Energy Method (DEM) is a novel numerical simulation method that combines deep learning and traditional energy methods to more accurately solve complex physical problems. DEM typically uses a deep neural network for modeling, training using forward and backward propagation algorithms, and minimizing potential energy with the help of artificial neural networks. Compared to traditional numerical methods, DEM has many advantages, such as being able to adaptively learn complex physical phenomena, fast convergence, and saving computational costs. Additionally, by improving the neural network architecture and training algorithm, the accuracy and efficiency of simulations can be further improved.
Many engineering problems involve energy functional issues, and the Deep Energy Method is a very flexible and efficient method because it only needs to define the energy function for analysis without solving equations. In addition, standard optimizers can find the minimum value through iterations without requiring tedious manual adjustments. This method uses the forward propagation process to perform unconstrained approximation, allowing for quick numerical analysis and being constrained by boundary conditions to form the final prediction.
Through solving coupled problems such as piezoelectric material beams and thermoelastic bodies, the effectiveness of this method has been verified and provides a new numerical analysis method.

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