A fundamental challenge in physics-informed machine learning (PIML) is the design of robust PIML methods for out-of-distribution (OOD) forecasting tasks. These OOD tasks require learning-to-learn from observations of the same (ODE) dynamical system with different unknown ODE parameters, and demand accurate forecasts even under out-of-support initial conditions and out-of-support ODE parameters. In this work we propose to improve the OOD robustness of PIML via a meta-learning procedure for causal structure discovery. Using three different OOD tasks, we empirically observe that the proposed approach significantly outperforms existing state-of-the-art PIML and deep learning methods (with $2\times$ to $28\times$ lower OOD errors).

Existing work in scientific machine learning (SciML) has shown that data-driven learning of solution operators can provide a fast approximate alternative to classical numerical partial differential equation (PDE) solvers. Of these, Neural Operators (NOs) have emerged as particularly promising. We observe that several uncertainty quantification (UQ) methods for NOs fail for test inputs that are even moderately out-of-domain (OOD), even when the model approximates the solution well for in-domain tasks. To address this limitation, we show that ensembling several NOs can identify high-error regions and provide good uncertainty estimates that are well-correlated with prediction errors. Based on this, we propose a cost-effective alternative, DiverseNO, that mimics the properties of the ensemble by encouraging diverse predictions from its multiple heads in the last feed-forward layer. We then introduce Operator-ProbConserv, a method that uses these well-calibrated UQ estimates within the ProbConserv framework to update the model. Our empirical results show that Operator-ProbConserv enhances OOD model performance for a variety of challenging PDE problems and satisfies physical constraints such as conservation laws.

In this work we generalize traditional node/link prediction tasks in dynamic heterogeneous networks, to consider joint prediction over larger k-node induced subgraphs. Our key insight is to incorporate the unavoidable dependencies in the training observations of induced subgraphs into both the input features and the model architecture itself via high-order dependencies. The strength of the representation is its invariance to isomorphisms and varying local neighborhood sizes, while still being able to take node/edge labels into account, and facilitating inductive reasoning (i.e., generalization to unseen portions of the network). Empirical results show that our proposed method significantly outperforms other state-of-the-art methods designed for static and/or single node/link prediction tasks. In addition, we show that our method is scalable and learns interpretable parameters.

Conversational recommender systems help users navigate through the product space by exploiting feedback. In conversational systems based on preference-based feedback, the user selects the most preferred item from a list of recommended products. Modelling user's preferences then becomes important in order to recommend relevant items. Several existing recommender systems accomplish this by assuming the features to be independent. Here we will attempt to forego this assumption and exploit the dependencies between the features to build a robust user preference model.