<p>Achieving superior polymeric components through additive manufacturing (AM) relies on precise control of rheology. One rheological property particularly relevant to AM is melt viscosity (<i>η</i>). <i>η</i> is influenced by polymer chemistry, molecular weight (<i>M</i><sub><i>w</i></sub>), polydispersity, shear rate (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1532_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{\gamma}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>γ</mi> </mrow> <mrow> <mo>̇</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>), and temperature (<i>T</i>). The relationship of <i>η</i> with <i>M</i><sub><i>w</i></sub>, <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1532_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{\gamma }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>γ</mi> </mrow> <mrow> <mo>̇</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>, and <i>T</i> is captured by parameterized equations. Several physical experiments are required to fit the parameters, so predicting <i>η</i> of new polymer materials in unexplored physical domains is laborious. Here, we develop a Physics-Enforced Neural Network (PENN) model that predicts the empirical parameters and encodes the parametrized equations to calculate <i>η</i> as a function of polymer chemistry, <i>M</i><sub><i>w</i></sub>, polydispersity, <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1532_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{\gamma }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>γ</mi> </mrow> <mrow> <mo>̇</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>, and <i>T</i>. We benchmark our PENN against physics-unaware Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) models. We demonstrate that the PENN offers superior values of <i>η</i> when extrapolating to unseen values of <i>M</i><sub><i>w</i></sub>, <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41524_2025_1532_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\({\dot{\gamma }}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mrow> <mi>γ</mi> </mrow> <mrow> <mo>̇</mo> </mrow> </mover> </math></EquationSource> </InlineEquation>, and <i>T</i> for sparsely seen polymers.</p>

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A physics-enforced neural network to predict polymer melt viscosity

  • Ayush Jain,
  • Rishi Gurnani,
  • Arunkumar Rajan,
  • H.Jerry Qi,
  • Rampi Ramprasad

摘要

Achieving superior polymeric components through additive manufacturing (AM) relies on precise control of rheology. One rheological property particularly relevant to AM is melt viscosity (η). η is influenced by polymer chemistry, molecular weight (Mw), polydispersity, shear rate ( \({\dot{\gamma}}\) γ ̇ ), and temperature (T). The relationship of η with Mw, \({\dot{\gamma }}\) γ ̇ , and T is captured by parameterized equations. Several physical experiments are required to fit the parameters, so predicting η of new polymer materials in unexplored physical domains is laborious. Here, we develop a Physics-Enforced Neural Network (PENN) model that predicts the empirical parameters and encodes the parametrized equations to calculate η as a function of polymer chemistry, Mw, polydispersity, \({\dot{\gamma }}\) γ ̇ , and T. We benchmark our PENN against physics-unaware Artificial Neural Network (ANN) and Gaussian Process Regression (GPR) models. We demonstrate that the PENN offers superior values of η when extrapolating to unseen values of Mw, \({\dot{\gamma }}\) γ ̇ , and T for sparsely seen polymers.