Physics-Enhanced Multi-fidelity Learning for Optical Surface Imprint

Abstract

Human fingerprints serve as one unique and powerful characteristic for each person, from which policemen can recognize the identity. Similar to humans, many natural bodies and intrinsic mechanical qualities can also be uniquely identified from surface characteristics. To measure the elasto-plastic properties of one material, one formally sharp indenter is pushed into the measured body under constant force and retracted, leaving a unique residual imprint of the minute size from several micrometers to nanometers. However, one great challenge is how to map the optical image of this residual imprint into the real wanted mechanical properties, \ie, the tensile force curve. In this paper, we propose a novel method to use multi-fidelity neural networks (MFNN) to solve this inverse problem. We first build up the NN model via pure simulation data, and then bridge the sim-to-real gap via transfer learning. Considering the difficulty of collecting real experimental data, we use NN to dig out the unknown physics and also implant the known physics into the transfer learning framework, thus highly improving the model stability and decreasing the data requirement. The final constructed model only needs three-shot calibration of real materials. We tested the final model across 20 real materials and achieved satisfying accuracy. This work serves as one great example of applying machine learning into scientific research, especially under the constraints of data limitation and fidelity variance.

Figures (11)

• Figure 1: Experimental methods. (A and B) Schematic illustrations of indentation and optical profilometer, respectively. (C) Typical pile-up image taken from scanning electron microscope. (D) Typical height distribution image measured by optical profilometer.
• Figure 2: Transfer learning to solve the indentation inverse problem via residual imprint (pile-up). (A) Schematic illustration of indentation forward and inverse problems. Materials conforming to typical hardening behaviors (left) will form pile-up on sample surfaces after indentation and response typical load-displacement curves (right). (B) Flowcharts of the transfer learning DNN employed in this study.
• Figure 3: 2D and 3D FEM models in our study. The total element number is 3449 in 2D FEM (A) and 223292 in 3D FEM (B).
• Figure 4: Forward prediction with the unique problem and inverse prediction with the feature selection process. (A) Forward prediction combining BFGS optimization to find the mystical material siblings with the same indentation features. (B1-B2) Two typical material siblings (($E, \sigma_y, n, K$) = (200, 0.28, 0.65, 1.365), (203, 0.254, 0.485, 1.020)) corresponding to almost the same load-displacement curves. (C) Plot of Non-unique ratio v.s., Distinguishing ratio. (D) Value correlation of the predicted $n$ and the target $n$. The results are based on 4000 2D FEM data with 3500 training data (blue) and 500 testing data (orange).
• Figure 5: Pile-up profiles acquired from experiments and simulations. (A-C) and (D-F) are pile-up profiles of SS304, and Al7075, respectively. (A) SS304 pile-up profile measured from experiments. The vertical heights of four-fold profiles are divided into slim square strips and averaged v.s., the horizontal distance (X, green color) from the origin. Both the heights and distances are normalized by the indentation lateral length (a, white color). All the 3D pile-up profiles (A-B, D-E) are dissolved through this method to form into 2D pile-up curves (C) and (F).