Each year the Association for the Advancement of Artificial Intelligence (AAAI) recognizes a group of individuals who have made significant, sustained contributions to the field of artificial intelligence by appointing them as Fellows. We've been talking to some of the 2024 AAAI Fellows to find out more about their research. In this interview, we meet Anima Anandkumar and find out about her work on Neural Operators, of which she is the inventor. Neural Operators are able to learn complex physical phenomena that occur at multiple resolutions while standard neural networks are unable to do so. Standard neural networks use a fixed number of pixels or resolution to learn a phenomenon, while neural operators represent data as continuous functions.

Deep Learning (DL), in particular deep neural networks (DNN), by design is purely data-driven and in general does not require physics. This is the strength of DL but also one of its key limitations when applied to science and engineering problems in which underlying physical properties--such as stability, conservation, and positivity--and desired accuracy need to be achieved. DL methods in their original forms are not capable of respecting the underlying mathematical models or achieving desired accuracy even in big-data regimes. On the other hand, many data-driven science and engineering problems, such as inverse problems, typically have limited experimental or observational data, and DL would overfit the data in this case. Leveraging information encoded in the underlying mathematical models, we argue, not only compensates missing information in low data regimes but also provides opportunities to equip DL methods with the underlying physics and hence obtaining higher accuracy. This short communication introduces several model-constrained DL approaches--including both feed-forward DNN and autoencoders--that are capable of learning not only information hidden in the training data but also in the underlying mathematical models to solve inverse problems. We present and provide intuitions for our formulations for general nonlinear problems. For linear inverse problems and linear networks, the first order optimality conditions show that our model-constrained DL approaches can learn information encoded in the underlying mathematical models, and thus can produce consistent or equivalent inverse solutions, while naive purely data-based counterparts cannot.