Digital twins have received significant attention and development in recent years due to the promise of enabling real-time design and analysis of complex systems. However, realizing this potential will require supplementing high-fidelity numerical representations with reduced-order and data-driven surrogate models that can be queried in real-time. Meanwhile, scientific machine learning is an emerging discipline that merges scientific computing and machine learning. Whilst scientific computing focuses on large-scale models that are derived from scientific laws describing physical phenomena, machine learning, including deep learning, focuses on developing data-driven models which require minimal knowledge and prior assumptions. With the contrast between these two approaches follows different advantages: scientific models are effective at extrapolation and can be fitted with small data and few parameters whereas deep learning models require a significant amount of data and a large number of parameters but are not biased by the validity of prior assumptions. Scientific machine learning endeavors to combine the two disciplines in order to develop models that retain the advantages from their respective disciplines. This mini-symposium collects recent works on scientific machine learning methods in the context of enabling real-time inference for digital twins. We anticipate contributions covering theories and algorithms for both forward and inverse problems with applications in engineering, sciences, and scientific computing.