Explaining artificial intelligence or machine learning models is increasingly important. To use such data-driven systems wisely we must understand how they interact with the world, including how they depend causally on data inputs. In this work we develop Causal Dependence Plots (CDPs) to visualize how one variable--an outcome--depends on changes in another variable--a predictor--$\textit{along with any consequent causal changes in other predictor variables}$. Crucially, CDPs differ from standard methods based on holding other predictors constant or assuming they are independent. CDPs make use of an auxiliary causal model because causal conclusions require causal assumptions. With simulations and real data experiments, we show CDPs can be combined in a modular way with methods for causal learning or sensitivity analysis. Since people often think causally about input-output dependence, CDPs can be powerful tools in the xAI or interpretable machine learning toolkit and contribute to applications like scientific machine learning and algorithmic fairness.

Bike sharing systems have been widely deployed around the world in recent years. A core problem in such systems is to reposition the bikes so that the distribution of bike supply is reshaped to better match the dynamic bike demand. When the bike-sharing company or platform is able to predict the revenue of each reposition task based on historic data, an additional constraint is to cap the payment for each task below its predicted revenue. In this paper, we propose an incentive mechanism called {\em TruPreTar} to incentivize users to park bicycles at locations desired by the platform toward rebalancing supply and demand. TruPreTar possesses four important economic and computational properties such as truthfulness and budget feasibility. Furthermore, we prove that even when the payment budget is tight, the total revenue still exceeds or equals the budget. Otherwise, TruPreTar achieves 2-approximation as compared to the optimal (revenue-maximizing) solution, which is close to the lower bound of at least $\sqrt{2}$ that we also prove. Using an industrial dataset obtained from a large bike-sharing company, our experiments show that TruPreTar is effective in rebalancing bike supply and demand and, as a result, generates high revenue that outperforms several benchmark mechanisms.

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady flows past moving bodies, such as flapping wings is scarce. Earlier studies mostly relied on transferring to a body attached frame of reference which is restrictive towards handling multiple moving bodies or deforming structures. Hence, in the present work, an immersed boundary aware framework has been explored for developing surrogate models for unsteady flows past moving bodies. Specifically, simultaneous pressure recovery and velocity reconstruction from Immersed boundary method (IBM) simulation data has been investigated. While, efficacy of velocity reconstruction has been tested against the fine resolution IBM data, as a step further, the pressure recovered was compared with that of an arbitrary Lagrange Eulerian (ALE) based solver. Under this framework, two PINN variants, (i) a moving-boundary-enabled standard Navier-Stokes based PINN (MB-PINN), and, (ii) a moving-boundary-enabled IBM based PINN (MB-IBM-PINN) have been formulated. A fluid-solid partitioning of the physics losses in MB-IBM-PINN has been allowed, in order to investigate the effects of solid body points while training. This enables MB-IBM-PINN to match with the performance of MB-PINN under certain loss weighting conditions. MB-PINN is found to be superior to MB-IBM-PINN when {\it a priori} knowledge of the solid body position and velocity are available. To improve the data efficiency of MB-PINN, a physics based data sampling technique has also been investigated. It is observed that a suitable combination of physics constraint relaxation and physics based sampling can achieve a model performance comparable to the case of using all the data points, under a fixed training budget.

A recent alternative for hydrogen transportation as a mixture with natural gas is blending it into natural gas pipelines. However, hydrogen embrittlement of material is a major concern for scientists and gas installation designers to avoid process failures. In this paper, we propose a physics-informed machine learning model to predict the gas pressure on the pipes' inner wall. Despite its high-fidelity results, the current PDE-based simulators are time- and computationally-demanding. Using simulation data, we train an ML model to predict the pressure on the pipelines' inner walls, which is a first step for pipeline system surveillance. We found that the physics-based method outperformed the purely data-driven method and satisfy the physical constraints of the gas flow system.

Recent years have witnessed the impressive progress in Neural Dependency Parsing. According to the different factorization approaches to the graph joint probabilities, existing parsers can be roughly divided into autoregressive and non-autoregressive patterns. The former means that the graph should be factorized into multiple sequentially dependent components, then it can be built up component by component. And the latter assumes these components to be independent so that they can be outputted in a one-shot manner. However, when treating the directed edge as an explicit dependency relationship, we discover that there is a mixture of independent and interdependent components in the dependency graph, signifying that both aforementioned models fail to precisely capture the explicit dependencies among nodes and edges. Based on this property, we design a Semi-Autoregressive Dependency Parser to generate dependency graphs via adding node groups and edge groups autoregressively while pouring out all group elements in parallel. The model gains a trade-off between non-autoregression and autoregression, which respectively suffer from the lack of target inter-dependencies and the uncertainty of graph generation orders. The experiments show the proposed parser outperforms strong baselines on Enhanced Universal Dependencies of multiple languages, especially achieving $4\%$ average promotion at graph-level accuracy. Also, the performances of model variations show the importance of specific parts.

Pre-trained machine learning (ML) models have shown great performance for a wide range of applications, in particular in natural language processing (NLP) and computer vision (CV). Here, we study how pre-training could be used for scientific machine learning (SciML) applications, specifically in the context of transfer learning. We study the transfer behavior of these models as (i) the pre-trained model size is scaled, (ii) the downstream training dataset size is scaled, (iii) the physics parameters are systematically pushed out of distribution, and (iv) how a single model pre-trained on a mixture of different physics problems can be adapted to various downstream applications. We find that-when fine-tuned appropriately-transfer learning can help reach desired accuracy levels with orders of magnitude fewer downstream examples (across different tasks that can even be out-of-distribution) than training from scratch, with consistent behavior across a wide range of downstream examples. We also find that fine-tuning these models yields more performance gains as model size increases, compared to training from scratch on new downstream tasks. These results hold for a broad range of PDE learning tasks. All in all, our results demonstrate the potential of the "pre-train and fine-tune" paradigm for SciML problems, demonstrating a path towards building SciML foundation models. We open-source our code for reproducibility.

The seventh asteroid, Justitia, is the most intriguing. About 30 miles wide, Justitia is very reddish, an unusual color for an asteroid. Indeed, it looks more like one of the small icy worlds found in the Kuiper belt, circling the sun beyond the orbit of Neptune. That has led planetary scientists to speculate that Justitia formed in the outer reaches of the solar system and then was scattered inward by the shifting orbits of the giant planets, eventually joining the asteroid belt. If that is true, a visit to Justitia would provide a close-up study of a Kuiper belt object without the long trip to the solar system's distant reaches.

This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the positive semi-definite -- PSD model) from which it is possible to obtain independent and identically distributed (i.i.d.) samples at precision $\varepsilon$ with a cost that is $m^2 d \log(1/\varepsilon)$ where $m$ is the dimension of the model, $d$ the dimension of the space. The proposed approach consists in: first, computing the PSD model that satisfies the Fokker-Planck equation (or its fractional variant) associated with the SDE, up to error $\varepsilon$, and then sampling from the resulting PSD model. Assuming some regularity of the Fokker-Planck solution (i.e. $\beta$-times differentiability plus some geometric condition on its zeros) We obtain an algorithm that: (a) in the preparatory phase obtains a PSD model with L2 distance $\varepsilon$ from the solution of the equation, with a model of dimension $m = \varepsilon^{-(d+1)/(\beta-2s)} (\log(1/\varepsilon))^{d+1}$ where $1/2\leq s\leq1$ is the fractional power to the Laplacian, and total computational complexity of $O(m^{3.5} \log(1/\varepsilon))$ and then (b) for Fokker-Planck equation, it is able to produce i.i.d.\ samples with error $\varepsilon$ in Wasserstein-1 distance, with a cost that is $O(d \varepsilon^{-2(d+1)/\beta-2} \log(1/\varepsilon)^{2d+3})$ per sample. This means that, if the probability associated with the SDE is somewhat regular, i.e. $\beta \geq 4d+2$, then the algorithm requires $O(\varepsilon^{-0.88} \log(1/\varepsilon)^{4.5d})$ in the preparatory phase, and $O(\varepsilon^{-1/2}\log(1/\varepsilon)^{2d+2})$ for each sample. Our results suggest that as the true solution gets smoother, we can circumvent the curse of dimensionality without requiring any sort of convexity.

Shape Memory Alloys (SMAs) are a class of smart materials that exhibit a macroscopic contraction of up to 5% when heated via an electric current. This effect can be exploited for the development of novel unconventional actuators. Despite having many features such as compactness, lightweight, and high energy density, commercial SMA wires are characterized by a highly nonlinear behavior, which manifests itself as a load-, temperature-, and rate-dependent hysteresis exhibiting a complex shape and minor loops. Accurate modeling and compensation of such hysteresis are fundamental for the development of high-performance SMA applications. In this work, we propose a new dynamical model to describe the complex hysteresis of polycrystalline SMA wires. The approach is based on a reformulation of the Muller-Achenbach-Seelecke model for uniaxial SMA wires within a hybrid dynamical framework. In this way, we can significantly reduce the numerical complexity and computation time without losing accuracy and physical interpretability. After describing the model, an extensive experimental validation campaign is carried out on a 75 {\mu}m diameter SMA wire specimen. The new hybrid model will pave the development of hybrid controllers and observers for SMA actuators.