Seismic inversion is essential for geophysical exploration and geological assessment, but it is inherently subject to significant uncertainty. This uncertainty stems primarily from the limited information provided by observed seismic data, which is largely a result of constraints in data collection geometry. As a result, multiple plausible velocity models can often explain the same set of seismic observations. In deep learning-based seismic inversion, uncertainty arises from various sources, including data noise, neural network design and training, and inherent data limitations. This study introduces a novel approach to uncertainty quantification in seismic inversion by integrating ensemble methods with importance sampling. By leveraging ensemble approach in combination with importance sampling, we enhance the accuracy of uncertainty analysis while maintaining computational efficiency. The method involves initializing each model in the ensemble with different weights, introducing diversity in predictions and thereby improving the robustness and reliability of the inversion outcomes. Additionally, the use of importance sampling weights the contribution of each ensemble sample, allowing us to use a limited number of ensemble samples to obtain more accurate estimates of the posterior distribution. Our approach enables more precise quantification of uncertainty in velocity models derived from seismic data. By utilizing a limited number of ensemble samples, this method achieves an accurate and reliable assessment of uncertainty, ultimately providing greater confidence in seismic inversion results.

Generative models trained at scale can now produce text, video, and more recently, scientific data such as crystal structures. In applications of generative approaches to materials science, and in particular to crystal structures, the guidance from the domain expert in the form of high-level instructions can be essential for an automated system to output candidate crystals that are viable for downstream research. In this work, we formulate end-to-end language-to-structure generation as a multi-objective optimization problem, and propose Generative Hierarchical Materials Search (GenMS) for controllable generation of crystal structures. GenMS consists of (1) a language model that takes high-level natural language as input and generates intermediate textual information about a crystal (e.g., chemical formulae), and (2) a diffusion model that takes intermediate information as input and generates low-level continuous value crystal structures. GenMS additionally uses a graph neural network to predict properties (e.g., formation energy) from the generated crystal structures. During inference, GenMS leverages all three components to conduct a forward tree search over the space of possible structures. Experiments show that GenMS outperforms other alternatives of directly using language models to generate structures both in satisfying user request and in generating low-energy structures. We confirm that GenMS is able to generate common crystal structures such as double perovskites, or spinels, solely from natural language input, and hence can form the foundation for more complex structure generation in near future.

Seasonal climate forecasts are commonly based on model runs from fully coupled forecasting systems that use Earth system models to represent interactions between the atmosphere, ocean, land and other Earth-system components. Recently, machine learning (ML) methods are increasingly being investigated for this task where large-scale climate variability is linked to local or regional temperature or precipitation in a linear or non-linear fashion. This paper investigates the use of interpretable ML methods to predict seasonal precipitation for East Africa in an operational setting. Dimension reduction is performed by decomposing the precipitation fields via empirical orthogonal functions (EOFs), such that only the respective factor loadings need to the predicted. Indices of large-scale climate variability--including the rate of change in individual indices as well as interactions between different indices--are then used as potential features to obtain tercile forecasts from an interpretable ML algorithm. Several research questions regarding the use of data and the effect of model complexity are studied. The results are compared against the ECMWF seasonal forecasting system (SEAS5) for three seasons--MAM, JJAS and OND--over the period 1993-2020. Compared to climatology for the same period, the ECMWF forecasts have negative skill in MAM and JJAS and significant positive skill in OND. The ML approach is on par with climatology in MAM and JJAS and a significantly positive skill in OND, if not quite at the level of the OND ECMWF forecast.

Generative large language models (LLMs) excel in natural language processing tasks, yet their inner workings remain underexplored beyond token-level predictions. This study investigates the degree to which these models decide the content of a paragraph at its onset, shedding light on their contextual understanding. By examining the information encoded in single-token activations, specifically the "\textbackslash n\textbackslash n" double newline token, we demonstrate that patching these activations can transfer significant information about the context of the following paragraph, providing further insights into the model's capacity to plan ahead.

This paper introduces a novel Soft Acoustic Curvature (SAC) sensor. SAC incorporates integrated audio components and features an acoustic channel within a flexible structure. A reference acoustic wave, generated by a speaker at one end of the channel, propagates and is received by a microphone at the other channel's end. Our previous study revealed that acoustic wave energy dissipation varies with acoustic channel deformation, leading us to design a novel channel capable of large deformation due to bending. We then use Machine Learning (ML) models to establish a complex mapping between channel deformations and sound modulation. Various sound frequencies and ML models were evaluated to enhance curvature detection accuracy. The sensor, constructed using soft material and 3D printing, was validated experimentally, with curvature measurement errors remaining within 3.5 m-1 for a range of 0 to 60 m-1 curvatures. These results demonstrate the effectiveness of the proposed method for estimating curvatures. With its flexible structure, the SAC sensor holds potential for applications in soft robotics, including shape measurement for continuum manipulators, soft grippers, and wearable devices.

As AI systems become more autonomous and capable, experts warn of them potentially causing catastrophic losses. Drawing on the successful precedent set by the nuclear power industry, this paper argues that developers of frontier AI models should be assigned limited, strict, and exclusive third party liability for harms resulting from Critical AI Occurrences (CAIOs) - events that cause or easily could have caused catastrophic losses. Mandatory insurance for CAIO liability is recommended to overcome developers' judgment-proofness, mitigate winner's curse dynamics, and leverage insurers' quasi-regulatory abilities. Based on theoretical arguments and observations from the analogous nuclear power context, insurers are expected to engage in a mix of causal risk-modeling, monitoring, lobbying for stricter regulation, and providing loss prevention guidance in the context of insuring against heavy-tail risks from AI. While not a substitute for regulation, clear liability assignment and mandatory insurance can help efficiently allocate resources to risk-modeling and safe design, facilitating future regulatory efforts.

Understanding the behavior of complex molecular systems is a fundamental problem in physical chemistry. To describe the long-time dynamics of such systems, which is responsible for their most informative characteristics, we can identify a few slow collective variables (CVs) while treating the remaining fast variables as thermal noise. This enables us to simplify the dynamics and treat it as diffusion in a free-energy landscape spanned by slow CVs, effectively rendering the dynamics Markovian. Our recent statistical learning technique, spectral map [Rydzewski, J. Phys. Chem. Lett. 2023, 14, 22, 5216-5220], explores this strategy to learn slow CVs by maximizing a spectral gap of a transition matrix. In this work, we introduce several advancements into our framework, using a high-dimensional reversible folding process of a protein as an example. We implement an algorithm for coarse-graining Markov transition matrices to partition the reduced space of slow CVs kinetically and use it to define a transition state ensemble. We show that slow CVs learned by spectral map closely approach the Markovian limit for an overdamped diffusion. We demonstrate that coordinate-dependent diffusion coefficients only slightly affect the constructed free-energy landscapes. Finally, we present how spectral map can be used to quantify the importance of features and compare slow CVs with structural descriptors commonly used in protein folding. Overall, we demonstrate that a single slow CV learned by spectral map can be used as a physical reaction coordinate to capture essential characteristics of protein folding.

The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .

Though current long-context large language models (LLMs) have demonstrated impressive capacities in answering user questions based on extensive text, the lack of citations in their responses makes user verification difficult, leading to concerns about their trustworthiness due to their potential hallucinations. In this work, we aim to enable long-context LLMs to generate responses with fine-grained sentence-level citations, improving their faithfulness and verifiability. We first introduce LongBench-Cite, an automated benchmark for assessing current LLMs' performance in Long-Context Question Answering with Citations (LQAC), revealing considerable room for improvement. To this end, we propose CoF (Coarse to Fine), a novel pipeline that utilizes off-the-shelf LLMs to automatically generate long-context QA instances with precise sentence-level citations, and leverage this pipeline to construct LongCite-45k, a large-scale SFT dataset for LQAC. Finally, we train LongCite-8B and LongCite-9B using the LongCite-45k dataset, successfully enabling their generation of accurate responses and fine-grained sentence-level citations in a single output. The evaluation results on LongBench-Cite show that our trained models achieve state-of-the-art citation quality, surpassing advanced proprietary models including GPT-4o.

Robotic grippers are the end effector in the robot system of handling any task which used for performing various operations for the purpose of industrial application and hazardous tasks.In this paper, we developed the mathematical model for multi fingers robotics grippers. we are concerned with Jamia'shand which is developed in Robotics Lab, Mechanical Engineering Deptt, Faculty of Engg & Technolgy, Jamia Millia Islamia, India. This is a tendon-driven gripper each finger having three DOF having a total of 11 DOF. The term tendon is widely used to imply belts, cables, or similar types of applications. It is made up of three fingers and a thumb. Every finger and thumb has one degree of freedom. The power transmission mechanism is a rope and pulley system. Both hands have similar structures. Aluminum from the 5083 families was used to make this product. The gripping force can be adjusted we have done the kinematics, force, and dynamic analysis by developing a Mathematical model for the four-finger robotics grippers and their thumb. we focused it control motions in X and Y Displacements with the angular positions movements and we make the force analysis of the four fingers and thumb calculate the maximum weight, force, and torque required to move it with mass. Draw the force -displacements graph which shows the linear behavior up to 250 N and shows nonlinear behavior beyond this. and required Dmin of wire is 0.86 mm for grasping the maximum 1 kg load also developed the dynamic model (using energy )approach lagrangian method to find it torque required to move the fingers.