逆向熱傳問題廣泛應用於工程領域中之熱源辨識與加熱源瓦數估測，然而此類問題本質上具有不適定性，對量測誤差與模型設定高度敏感，傳統數值方法在求解過程中往往需反覆進行正向模擬，導致計算成本高且穩定性受限。隨著深度學習技術之發展，物理資訊神經網路（Physics-Informed Neural Network, PINN）透過將物理控制方程嵌入神經網路訓練過程，為解決逆向熱傳問題提供一種具潛力之新方法。
本研究針對三維暫態熱傳系統，建立一套結合 PINN 之逆向分析架構，以有限溫度量測資料推估未知加熱源，並與傳統計算流體力學（Computational Fluid Dynamics, CFD）結合最小平方法之逆向分析方法進行比較分析。在方法上，本研究將熱傳統御方程式、初始條件及邊界條件納入損失函數中，並結合量測溫度資料作為資料約束，使模型能於單一神經網路架構下，同時完成暫態溫度場重建與未知加熱源之預測。此外，為確保模型之穩定性與準確性，針對網路維度、學習率以及資料損失與物理損失之權重配置等關鍵超參數進行系統性分析，以篩選最佳參數組合。
在驗證方面，本研究分別於定發熱量與暫態變發熱量條件下進行測試，並以實驗量測資料作為參考解進行評估。結果顯示，PINN 在溫度場預測方面具有良好準確度，不論於訓練點或未參與訓練之驗證點（Ts2），其誤差均顯著低於 CFD，顯示模型具備良好之空間泛化能力。在未知加熱源預測方面，PINN 預測結果與參考值之差異亦顯著小於 CFD，並在多數時間點維持穩定且低誤差之表現。
進一步分析暫態變加熱源條件可發現，在加熱源瓦數快速變化階段，由於熱傳導過程存在時間延遲與材料熱慣性效應，導致逆向問題難度提升，所有方法之誤差皆有所增加。然而，相較於 CFD，PINN 仍能維持較低之誤差幅度與較佳之穩定性，顯示其結合物理約束與資料驅動之特性能有效提升預測結果之可靠性。在系統趨於穩定後，PINN 預測結果可高度接近參考解，顯示其於不同暫態條件下均具備良好適用性。
在計算效率方面，傳統 CFD 方法需進行長時間之數值模擬，且於預測過程中需多次重複計算；相較之下，PINN 僅需單次訓練即可完成整體分析，本研究中其計算時間由數週縮短至數十分鐘，顯示顯著之效率優勢。
綜合而言，本研究證實 PINN 能在有限量測資料條件下，同時準確重建暫態溫度場並有效預測未知加熱源，且在預測準確度、穩定性與計算效率上皆優於傳統數值方法，顯示其於逆向熱傳問題與相關工程應用中具有高度發展潛力。

Inverse heat conduction problems (IHCPs) are widely encountered in thermal engineering applications, such as electronic cooling systems, aerospace thermal protection, battery thermal management, and industrial heating processes. Since the heat flux on a heated surface cannot usually be measured directly, it must be estimated from limited temperature measurements through inverse analysis. Conventional inverse methods generally combine computational fluid dynamics (CFD) simulations with iterative optimization algorithms. Although these approaches can provide satisfactory predictions, repeated forward simulations significantly increase the computational cost, particularly for transient three-dimensional problems.
Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving both forward and inverse partial differential equation problems. By incorporating governing equations, boundary conditions, and experimental observations into a unified loss function, PINNs can simultaneously satisfy physical laws and measurement data while avoiding repeated numerical iterations. Consequently, PINNs provide an efficient framework for solving inverse heat transfer problems with sparse experimental data.
In this study, a PINN framework is developed to estimate the unknown transient heat flux applied to a three-dimensional horizontal composite plate. The network integrates the transient heat conduction equation, initial conditions, boundary conditions, and experimental temperature measurements into the training process. Two heating conditions, including constant heat flux and time-varying heat flux, are investigated to evaluate the prediction capability of the proposed model. The predicted heat fluxes and reconstructed temperature fields are compared with those obtained using a conventional CFD-based inverse method and experimental measurements.
The results demonstrate that the proposed PINN accurately reconstructs both constant and transient heat flux histories while maintaining excellent agreement with experimental temperature measurements. Furthermore, the predicted temperatures at validation locations not included in the training process agree well with the measured data, indicating satisfactory generalization capability. Compared with the conventional inverse CFD method, the proposed PINN achieves higher prediction accuracy while eliminating repeated forward simulations, thereby significantly improving computational efficiency.These results demonstrate that PINNs provide an effective and reliable alternative for solving three-dimensional transient inverse heat conduction problems.

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