SIKIŞTIRILAMAZ ISIL TAŞINIM PROBLEMLERİNİN FİZİKLE ÖĞRENEN YAPAY SİNİR AĞLARI İLE ÇÖZÜMÜ

Abstract

Fizikle öğrenen yapay sinir ağları (PINN'ler), etkinlikleri ve karmaşık ağlar oluşturmadan problemlerin üstesinden gelme yetenekleri nedeniyle son yıllarda mühendislik problemlerinde dikkat çekmiştir. PINN'ler, koruma yasalarında diferansiyel operatörleri değerlendirmek için otomatik türevlenmeyi kullanır ve bu nedenle bir ayrıklaştırma şemasına ihtiyaç duymaz. Bu yeteneği kullanarak, PINN'ler herhangi bir eğitim verisi olmadan kayıp fonksiyonunda geçerli fizik yasalarını karşılar. Bu çalışmada, gerçek uygulamalar ve karşılaştırılabilir sayısal veya analitik sonuçlara sahip problemler de dahil olmak üzere çeşitli sıkıştırılamaz ısıl taşınım problemlerini çözüyoruz. Modelin performansını değerlendirmek için analitik çözümü olan bir kanal problemini çözüyoruz. Model, bireysel kayıp terimlerinin ağırlıklarına büyük ölçüde bağımlıdır. Alan içindeki akış çok karmaşık değilse, sınır koşulu kaybının ağırlığının arttırılması doğruluğu artırır. Farklı tipteki ağların performansını ve Neumann sınır koşullarını yakalama yeteneğini değerlendirmek için, sınırlardaki sıcaklık gradyanlarından dolayı akışın meydana geldiği kapalı bir muhafazada bir termal konveksiyon problemini çözüyoruz. Basit tam bağlantılı ağ, termal konveksiyon problemlerinde iyi performans gösterir ve çok ölçekli davranış olmadığından ağda Fourier dönüşümüne ihtiyacımız yoktur. Son olarak, endüstriyel uygulamaları güç elektroniğine benzeyen sabit ve kararsız kısmen bloke kanal problemlerini ele alıyoruz ve yöntemin geçici problemlere de uygulanabileceğini gösteriyoruz.

Keywords

• fizikle öğrenen yapay sinir ağları
• makine öğrenmesi
• otomatik türevlenme
• sıkıştırılamaz
• ısı transferi.

PHYSICS INFORMED NEURAL NETWORKS FOR TWO DIMENSIONAL INCOMPRESSIBLE THERMAL CONVECTION PROBLEMS

Abstract

Physics-informed neural networks (PINNs) have drawn attention in recent years in engineering problems due to their effectiveness and ability to tackle problems without generating complex meshes. PINNs use automatic differentiation to evaluate differential operators in conservation laws and hence do not need a discretization scheme. Using this ability, PINNs satisfy governing laws of physics in the loss function without any training data. In this work, we solve various incompressible thermal convection problems, and compare the results with numerical or analytical results. To evaluate the accuracy of the model we solve a channel problem with an analytical solution. The model is highly dependent on the weights of individual loss terms. Increasing the weight of boundary condition loss improves the accuracy if the flow inside the domain is not complicated. To assess the performance of different type of networks and ability to capture the Neumann boundary conditions, we solve a thermal convection problem in a closed enclosure in which the flow occurs due to the temperature gradients on the boundaries. The simple fully connected network performs well in thermal convection problems, and we do not need a Fourier mapping in the network since there is no multiscale behavior. Lastly, we consider steady and unsteady partially blocked channel problems resembling industrial applications to power electronics and show that the method can be applied to transient problems as well.

Keywords

• physics-informed neural networks
• machine learning
• automatic differentiation
• incompressible
• heat transfer.

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