The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this task, we aim to identify a coordinate transformation that allows us to represent the dynamics of nonlinear systems using a common, simple model structure. The …

Stochastic optimal control, which has the goal of driving the behavior of noisy systems, is broadly applicable in science, engineering and artificial intelligence. Our work introduces Stochastic Optimal Control Matching (SOCM), a novel Iterative Diffusion Optimization (IDO) technique for stochastic optimal control that stems from the same philosophy as the conditional score matching loss for …

Undeniably, Large Language Models (LLMs) have stirred an extraordinary wave of innovation in the machine learning research domain, resulting in substantial impact across diverse fields such as reinforcement learning, robotics, and computer vision. Their incorporation has been rapid and transformative, marking a significant paradigm shift in the field of machine learning research. However, the …

We introduce Sequential Neural Posterior Score Estimation (SNPSE) and Sequential Neural Likelihood Score Estimation (SNLSE), two new score-based methods for Bayesian inference in simulator-based models. Our methods, inspired by the success of score-based methods in generative modelling, leverage conditional score-based diffusion models to generate samples from the posterior distribution of …

Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current simulation-based amortized inference methods are simulation-hungry and inflexible: They require the specification of a fixed parametric prior, simulator, and inference tasks …

In many neural networks, different values of the parameters may result in the same loss value. Parameter space symmetries are loss-invariant transformations that change the model parameters. Teleportation applies such transformations to accelerate optimization. However, the exact mechanism behind this algorithm’s success is not well understood. In this paper, we show that teleportation not only …

We investigate the CLIP image encoder by analyzing how individual model components affect the final representation. We decompose the image representation as a sum across individual image patches, model layers, and attention heads, and use CLIP's text representation to interpret the summands. Interpreting the attention heads, we characterize each head's role by automatically finding text …

Deep neural operators, such as DeepONet, have changed the paradigm in high-dimensional nonlinear regression, paving the way for significant generalization and speed-up in computational engineering applications. Here, we investigate the use of DeepONet to infer flow fields around unseen airfoils with the aim of shape constrained optimization, an important design problem in aerodynamics that …

Fine-tuning large language models (LLMs) with classic first-order optimizers entails prohibitive GPU memory due to the backpropagation process. Recent works have turned to zeroth-order optimizers for fine-tuning, which save substantial memory by using two forward passes. However, these optimizers are plagued by the heterogeneity of parameter curvatures across different dimensions. In this work, we …

Accurate error estimation is crucial in model order reduction, to obtain small reduced-order models as well as to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation approaches, knowledge about the time integration scheme is mandatory, e.g., the residual-based error estimators proposed for the reduced basis method. This …

Accurate error estimation is crucial in model order reduction, to obtain small reduced-order models as well as to certify their accuracy when deployed in downstream applications such as digital twins. In existing a posteriori error estimation approaches, knowledge about the time integration scheme is mandatory, e.g., the residual-based error estimators proposed for the reduced basis method. This …

Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since many different source distributions might produce the same distribution of data-consistent simulations. To make a principled choice among many equally valid …

This paper explores challenges in training Physics-Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in minimizing the PINN loss function, particularly due to ill-conditioning caused by differential operators in the residual term. We compare gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-BFGS, showing …

Simulation-based inference (SBI) provides a powerful framework for inferring posterior distributions of stochastic simulators in a wide range of domains. In many settings, however, the posterior distribution is not the end goal itself -- rather, the derived parameter values and their uncertainties are used as a basis for deciding what actions to take. Unfortunately, because posterior distributions …

Solving partial differential equations (PDEs) by learning the solution operators has emerged as an attractive alternative to traditional numerical methods. However, implementing such architectures presents two main challenges: flexibility in handling irregular and arbitrary input and output formats and scalability to large discretizations. Most existing architectures are limited by their desired …

We show that Deep Neural Networks introduce two heteroscedastic Gumbel noise sources into Q-Learning. To account for these noise sources, we propose Double Gumbel Q-Learning, a Deep Q-Learning algorithm applicable for both discrete and continuous control. In discrete control, we derive a closed-form expression for the loss function of our algorithm. In continuous control, this loss function is …

Simulation-based inference (SBI) is constantly in search of more expressive algorithms for accurately inferring the parameters of complex models from noisy data. We present consistency models for neural posterior estimation (CMPE), a new free-form conditional sampler for scalable, fast, and amortized SBI with generative neural networks. CMPE combines the advantages of normalizing flows and flow …

Global medium-range weather forecasting is critical to decision-making across many social and economic domains. Traditional numerical weather prediction uses increased compute resources to improve forecast accuracy, but cannot directly use historical weather data to improve the underlying model. We introduce a machine learning-based method called "GraphCast", which can be trained directly from …

Data valuation has found various applications in machine learning, such as data filtering, efficient learning and incentives for data sharing. The most popular current approach to data valuation is the Shapley value. While popular for its various applications, Shapley value is computationally expensive even to approximate, as it requires repeated iterations of training models on different subsets …

Recently, operator learning, or learning mappings between infinite-dimensional function spaces, has garnered significant attention, notably in relation to learning partial differential equations from data. Conceptually clear when outlined on paper, neural operators necessitate discretization in the transition to computer implementations. This step can compromise their integrity, often causing them …

Simulation-based inference (SBI) enables amortized Bayesian inference for simulators with implicit likelihoods. But when we are primarily interested in the quality of predictive simulations, or when the model cannot exactly reproduce the observed data (i.e., is misspecified), targeting the Bayesian posterior may be overly restrictive. Generalized Bayesian Inference (GBI) aims to robustify …

Machine learning research has long focused on models rather than datasets, and prominent datasets are used for common ML tasks without regard to the breadth, difficulty, and faithfulness of the underlying problems. Neglecting the fundamental importance of data has given rise to inaccuracy, bias, and fragility in real-world applications, and research is hindered by saturation across existing …

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of PDEs. Here, we present novel adaptations for convolutional neural networks to demonstrate that they are indeed able to process functions as inputs and outputs. …

Data valuation, especially quantifying data value in algorithmic prediction and decision-making, is a fundamental problem in data trading scenarios. The most widely used method is to define the data Shapley and approximate it by means of the permutation sampling algorithm. To make up for the large estimation variance of the permutation sampling that hinders the development of the data marketplace, …

{KFAC,EKFAC,Diagonal,Implicit} Fisher Matrices and finite width NTKs in PyTorch

Typical diffusion models are trained to accept a particular form of conditioning, most commonly text, and cannot be conditioned on other modalities without retraining. In this work, we propose a universal guidance algorithm that enables diffusion models to be controlled by arbitrary guidance modalities without the need to retrain any use-specific components. We show that our algorithm successfully …

Quantifying the impact of training data points is crucial for understanding the outputs of machine learning models and for improving the transparency of the AI pipeline. The influence function is a principled and popular data attribution method, but its computational cost often makes it challenging to use. This issue becomes more pronounced in the setting of large language models and text-to-image …

Contrastive Language-Image Pre-training (CLIP) is an approach that has advanced research and applications in computer vision, fueling modern recognition systems and generative models. We believe that the main ingredient to the success of CLIP is its \textit{data} and \textit{not} the \textit{model} architecture or pre-training {objective}. However, CLIP only provides very limited information about …

Intelligent tutoring systems optimize the selection and timing of learning materials to enhance understanding and long-term retention. This requires estimates of both the learner's progress ("knowledge tracing"; KT), and the prerequisite structure of the learning domain ("knowledge mapping"). While recent deep learning models achieve high KT accuracy, they do so at the expense of the …

Neuronal manifold learning techniques represent high-dimensional neuronal dynamics in low-dimensional embeddings to reveal the intrinsic structure of neuronal manifolds. Common to these techniques is their goal to learn low-dimensional embeddings that preserve all dynamic information in the high-dimensional neuronal data, i.e., embeddings that allow for reconstructing the original data. We …