The dataset is obtained from Li et al. (2022a), which consists of an interpolated dataset of Fourier layers with mode 12 and width 32 are used. F-FNO: Following the settings in Li et al. (2022a), we train the F-FNO model (Li et al., UNet: Analogous to the setup in Li et al. (2022a), we train a UNet model (Ronneberger A typical training curve can be found in Figure 8. Table 4: The per-epoch runtime (in seconds) of selected models for the hyperelasticity problem. We note that the numbers of trainable parameters for the "Geo-FNO" and "FNO" cases are different from The airfoil dataset is directly taken from Li et al. (2022a), which is an interpolated dataset of The physical parameters used in generating the data are: Y oung's modulus Symmetry is enforced only when the topology characteristic function χ is updated. Besides the resolution-independence property of DAFNO as shown in Figure 3, we further investigate the generalizability of DAFNO in both physical and temporal resolutions with this example. Specifically, the eDAFNO model is trained on a spatial resolution of 64 64 and a time step of 0.02 Our results show that eDAFNO prediction remains independent of the time step employed.

As societal awareness of climate change grows, corporate climate policy engagements are attracting attention.

We did not find significant difference between the two datasets.

The growth and characterization of materials using empirical optimization typically requires a significant amount of expert time, experience, and resources. Several complementary characterization methods are routinely performed to determine the quality and properties of a grown sample. Machine learning (ML) can support the conventional approaches by using historical data to guide and provide speed and efficiency to the growth and characterization of materials. Specifically, ML can provide quantitative information from characterization data that is typically obtained from a different modality. In this study, we have investigated the feasibility of projecting the quantitative metric from microscopy measurements, such as atomic force microscopy (AFM), using data obtained from spectroscopy measurements, like Raman spectroscopy. Generative models were also trained to generate the full and specific features of the Raman and photoluminescence spectra from each other and the AFM images of the thin film MoS$_2$. The results are promising and have provided a foundational guide for the use of ML for the cross-modal characterization of materials for their accelerated, efficient, and cost-effective discovery.

A key problem in deep learning is data e ffi ciency.