Machine Learning has demonstrated transformative potential in diverse scientific fields, with deep learning standing out for its exceptional performance [1]. However, the black-box nature of these deep learning models has raised concerns about their lack of physical interpretability. In an endeavor to bridge this interpretability gap, sophisticated methodologies such as Physics-Informed Neural Networks (PINNs) [2], DeepONet [3], symbolic regression [4], Scientific Machine Learning (Sci-ML) [5], and differentiable programming [6] are an attempt to solve this issue. This symposium seeks to bring together experts for an in-depth discussion on approaches that integrate domain-specific physical laws and principles directly into machine learning algorithms, thereby fostering a more interpretable and reliable modeling framework. [1] LeCun, Y., Bengio, Y., & Hinton, G. (2015). Deep learning. Nature, 521(7553), 436-444. [2] Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707. [3] Lu, L., Meng, X., Mao, Z., & Karniadakis, G. E. (2021). DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators. Nature Machine Intelligence, 3(5), 389-405. [4] Rudy, S. H., Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2017). Data-driven discovery of partial differential equations. Science advances, 3(4), e1602614. [5] Raissi, M., Yazdani, A., & Karniadakis, G. E. (2020). Hidden Fluid Mechanics: Learning Velocity and Pressure Fields from Flow Visualizations. Science, 367(6481), 1026-1030. [6] Innes, M., Edelman, A., Fischer, K., Rackauckas, C., Saba, E., Shah, V.B. and Tebbutt, W., 2019. A differentiable programming system to bridge machine learning and scientific computing. arXiv preprint arXiv:1907.07587.