In complex traffic environments, autonomous vehicles face multi-modal uncertainty about other agents' future behavior. To address this, recent advancements in learningbased motion predictors output multi-modal predictions. We present our novel framework that leverages Branch Model Predictive Control(BMPC) to account for these predictions. The framework includes an online scenario-selection process guided by topology and collision risk criteria. This efficiently selects a minimal set of predictions, rendering the BMPC realtime capable. Additionally, we introduce an adaptive decision postponing strategy that delays the planner's commitment to a single scenario until the uncertainty is resolved. Our comprehensive evaluations in traffic intersection and random highway merging scenarios demonstrate enhanced comfort and safety through our method.

This review article highlights state-of-the-art data-driven techniques to discover, encode, surrogate, or emulate constitutive laws that describe the path-independent and path-dependent response of solids. Our objective is to provide an organized taxonomy to a large spectrum of methodologies developed in the past decades and to discuss the benefits and drawbacks of the various techniques for interpreting and forecasting mechanics behavior across different scales. Distinguishing between machine-learning-based and model-free methods, we further categorize approaches based on their interpretability and on their learning process/type of required data, while discussing the key problems of generalization and trustworthiness. We attempt to provide a road map of how these can be reconciled in a data-availability-aware context. We also touch upon relevant aspects such as data sampling techniques, design of experiments, verification, and validation.

Drug discovery is a complex process that involves sequentially screening and examining a vast array of molecules to identify those with the target properties. This process, also referred to as sequential experimentation, faces challenges due to the vast search space, the rarity of target molecules, and constraints imposed by limited data and experimental budgets. To address these challenges, we introduce a human-in-the-loop framework for sequential experiments in drug discovery. This collaborative approach combines human expert knowledge with deep learning algorithms, enhancing the discovery of target molecules within a specified experimental budget. The proposed algorithm processes experimental data to recommend both promising molecules and those that could improve its performance to human experts. Human experts retain the final decision-making authority based on these recommendations and their domain expertise, including the ability to override algorithmic recommendations. We applied our method to drug discovery tasks using real-world data and found that it consistently outperforms all baseline methods, including those which rely solely on human or algorithmic input. This demonstrates the complementarity between human experts and the algorithm. Our results provide key insights into the levels of humans' domain knowledge, the importance of meta-knowledge, and effective work delegation strategies. Our findings suggest that such a framework can significantly accelerate the development of new vaccines and drugs by leveraging the best of both human and artificial intelligence.

Accurate representations of unknown and sub-grid physical processes through parameterizations (or closure) in numerical simulations with quantified uncertainty are critical for resolving the coarse-grained partial differential equations that govern many problems ranging from weather and climate prediction to turbulence simulations. Recent advances have seen machine learning (ML) increasingly applied to model these subgrid processes, resulting in the development of hybrid physics-ML models through the integration with numerical solvers. In this work, we introduce a novel framework for the joint estimation of physical parameters and machine learning parameterizations with uncertainty quantification. Our framework incorporates online training and efficient Bayesian inference within a high-dimensional parameter space, facilitated by differentiable programming. This proof of concept underscores the substantial potential of differentiable programming in synergistically combining machine learning with differential equations, thereby enhancing the capabilities of hybrid physics-ML modeling.

A two-wheeled self-balancing robot (TWSBR) is non-linear and unstable system. This study compares the performance of model-based and data-based control strategies for TWSBRs, with an explicit practical educational approach. Model-based control (MBC) algorithms such as Lead-Lag and PID control require a proficient dynamic modeling and mathematical manipulation to drive the linearized equations of motions and develop the appropriate controller. On the other side, data-based control (DBC) methods, like fuzzy control, provide a simpler and quicker approach to designing effective controllers without needing in-depth understanding of the system model. In this paper, the advantages and disadvantages of both MBC and DBC using a TWSBR are illustrated. All controllers were implemented and tested on the OSOYOO self-balancing kit, including an Arduino microcontroller, MPU-6050 sensor, and DC motors. The control law and the user interface are constructed using the LabVIEW-LINX toolkit. A real-time hardware-in-loop experiment validates the results, highlighting controllers that can be implemented on a cost-effective platform.

Uncertainty has long been a critical area of study in robotics, particularly when robots are equipped with analytical models. As we move towards the widespread use of deep neural networks in robots, which have demonstrated remarkable performance in research settings, understanding the nuances of uncertainty becomes crucial for their real-world deployment. This guide offers an overview of the importance of uncertainty and provides methods to quantify and evaluate it from an applications perspective.

Fine-tuned Large Language Models (LLMs) often suffer from overconfidence and poor calibration, particularly when fine-tuned on small datasets. To address these challenges, we propose a simple combination of Low-Rank Adaptation (LoRA) with Gaussian Stochastic Weight Averaging (SWAG), facilitating approximate Bayesian inference in LLMs. Through extensive testing across several Natural Language Processing (NLP) benchmarks, we demonstrate that our straightforward and computationally efficient approach improves model generalization and calibration competitively with comparable, more sophisticated methods for Bayesian inference in LLMs. We further show that our method exhibits greater robustness against distribution shift, as reflected in its performance on out-of-distribution tasks.

The need to analyze sensitive data, such as medical records or financial data, has created a critical research challenge in recent years. In this paper, we adopt the framework of differential privacy, and explore mechanisms for generating an entire dataset which accurately captures characteristics of the original data. We build upon the work of Boedihardjo et al, which laid the foundations for a new optimization-based algorithm for generating private synthetic data. Importantly, we adapt their algorithm by replacing a uniform sampling step with a private distribution estimator; this allows us to obtain better computational guarantees for discrete distributions, and develop a novel algorithm suitable for continuous distributions. We also explore applications of our work to several statistical tasks.

Finding low-dimensional interpretable models of complex physical fields such as turbulence remains an open question, 80 years after the pioneer work of Kolmogorov. Estimating high-dimensional probability distributions from data samples suffers from an optimization and an approximation curse of dimensionality. It may be avoided by following a hierarchic probability flow from coarse to fine scales. This inverse renormalization group is defined by conditional probabilities across scales, renormalized in a wavelet basis. For a $\varphi^4$ scalar potential, sampling these hierarchic models avoids the critical slowing down at the phase transition. An outstanding issue is to also approximate non-Gaussian fields having long-range interactions in space and across scales. We introduce low-dimensional models with robust multiscale approximations of high order polynomial energies. They are calculated with a second wavelet transform, which defines interactions over two hierarchies of scales. We estimate and sample these wavelet scattering models to generate 2D vorticity fields of turbulence, and images of dark matter densities.

In this paper, we present a novel approach to accelerate the Bayesian inference process, focusing specifically on the nested sampling algorithms. Bayesian inference plays a crucial role in cosmological parameter estimation, providing a robust framework for extracting theoretical insights from observational data. However, its computational demands can be substantial, primarily due to the need for numerous likelihood function evaluations. Our proposed method utilizes the power of deep learning, employing feedforward neural networks to approximate the likelihood function dynamically during the Bayesian inference process. Unlike traditional approaches, our method trains neural networks on-the-fly using the current set of live points as training data, without the need for pre-training. This flexibility enables adaptation to various theoretical models and datasets. We perform simple hyperparameter optimization using genetic algorithms to suggest initial neural network architectures for learning each likelihood function. Once sufficient accuracy is achieved, the neural network replaces the original likelihood function. The implementation integrates with nested sampling algorithms and has been thoroughly evaluated using both simple cosmological dark energy models and diverse observational datasets. Additionally, we explore the potential of genetic algorithms for generating initial live points within nested sampling inference, opening up new avenues for enhancing the efficiency and effectiveness of Bayesian inference methods.