Coupled partial differential equations (PDEs) are key tasks in modeling the complex dynamics of many physical processes. Recently, neural operators have shown the ability to solve PDEs by learning the integral kernel directly in Fourier/Wavelet space, so the difficulty for solving the coupled PDEs depends on dealing with the coupled mappings between the functions. Towards this end, we propose a coupled multiwavelets neural operator (CMWNO) learning scheme by decoupling the coupled integral kernels during the multiwavelet decomposition and reconstruction procedures in the Wavelet space. The proposed model achieves significantly higher accuracy compared to previous learning-based solvers in solving the coupled PDEs including Gray-Scott (GS) equations and the non-local mean field game (MFG) problem. According to our experimental results, the proposed model exhibits a 2ˆ 4ˆ improvement relative L2 error compared to the best results from the state-of-the-art models. Human perception relies on detecting and processing waves. While our eyes detect waves of electromagnetic radiation, our ears detect waves of compression in the surrounding air.

Near-term quantum systems tend to be noisy. Crosstalk noise has been recognized as one of several major types of noises in superconducting Noisy Intermediate-Scale Quantum (NISQ) devices. Crosstalk arises from the concurrent execution of two-qubit gates on nearby qubits, such as \texttt{CX}. It might significantly raise the error rate of gates in comparison to running them individually. Crosstalk can be mitigated through scheduling or hardware machine tuning. Prior scientific studies, however, manage crosstalk at a really late phase in the compilation process, usually after hardware mapping is done. It may miss great opportunities of optimizing algorithm logic, routing, and crosstalk at the same time. In this paper, we push the envelope by considering all these factors simultaneously at the very early compilation stage. We propose a crosstalk-aware quantum program compilation framework called CQC that can enhance crosstalk mitigation while achieving satisfactory circuit depth. Moreover, we identify opportunities for translation from intermediate representation to the circuit for application-specific crosstalk mitigation, for instance, the \texttt{CX} ladder construction in variational quantum eigensolvers (VQE). Evaluations through simulation and on real IBM-Q devices show that our framework can significantly reduce the error rate by up to 6$\times$, with only $\sim$60\% circuit depth compared to state-of-the-art gate scheduling approaches. In particular, for VQE, we demonstrate 49\% circuit depth reduction with 9.6\% fidelity improvement over prior art on the H4 molecule using IBMQ Guadalupe. Our CQC framework will be released on GitHub.

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 matching methods into a single generative architecture: It essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be tailored to the structure of the estimation problem. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on three hard low-dimensional problems, but also achieves competitive performance in a high-dimensional Bayesian denoising experiment and in estimating a computationally demanding multi-scale model of tumor spheroid growth.

Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.

In this paper, we propose a generic algorithm to train machine learning-based subgrid parametrizations online, i.e., with a posteriori loss functions, but for non-differentiable numerical solvers. The proposed approach leverages a neural emulator to approximate the reduced state-space solver, which is then used to allow gradient propagation through temporal integration steps. We apply this methodology on a single layer quasi-geostrophic system with topography, known to be highly unstable in around 500 temporal iterations with offline strategies. Using our algorithm, we are able to train a parametrization that recovers most of the benefits of online strategies without having to compute the gradient of the original solver. It is demonstrated that training the neural emulator and parametrization components separately with different loss quantities is necessary in order to minimize the propagation of approximation biases. Experiments on emulator architectures with different complexities also indicates that emulator performance is key in order to learn an accurate parametrization. This work is a step towards learning parametrization with online strategies for realistic climate models.

Accurately modeling their mechanical response is challenging and computationally demanding, especially for inelastic behavior. To address the computational burden, we have developed a Recurrent Neural Network (RNN) model as a surrogate for meso-scale simulations. As a basis for RNN training, a mean-field model generates a comprehensive data set representing elasto-plastic behavior. Arbitrary six-dimensional time histories of strain are used to generate multiaxial stress-strain histories under random walking and cyclic loading conditions as the source and target tasks, respectively. First, the RNN model is trained for the source task. The same model is trained leveraging transfer learning for the target task, containing fewer data and sparse features because only some strain components are non-zero. The candidate model is successfully trained and validated through a grid search exploration of over 220 different RNN configurations and demonstrates accurate predictions for both source and target tasks. The results demonstrate that transfer learning could be used to train the RNN effectively under varying strain conditions and arbitrary constituents' material properties, suggesting its potential as an appropriate tool for modeling path-dependent responses in woven composites.

The increasing use of stochastic models for describing complex phenomena warrants surrogate models that capture the reference model characteristics at a fraction of the computational cost, foregoing potentially expensive Monte Carlo simulation. The predominant approach of fitting a large neural network and then pruning it to a reduced size has commonly neglected shortcomings. The produced surrogate models often will not capture the sensitivities and uncertainties inherent in the original model. In particular, (higher-order) derivative information of such surrogates could differ drastically. Given a large enough network, we expect this derivative information to match. However, the pruned model will almost certainly not share this behavior. In this paper, we propose to find surrogate models by using sensitivity information throughout the learning and pruning process. We build on work using Interval Adjoint Significance Analysis for pruning and combine it with the recent advancements in Sobolev Training to accurately model the original sensitivity information in the pruned neural network based surrogate model. We experimentally underpin the method on an example of pricing a multidimensional Basket option modelled through a stochastic differential equation with Brownian motion. The proposed method is, however, not limited to the domain of quantitative finance, which was chosen as a case study for intuitive interpretations of the sensitivities. It serves as a foundation for building further surrogate modelling techniques considering sensitivity information.

Despite its exceptional soft tissue contrast, Magnetic Resonance Imaging (MRI) faces the challenge of long scanning times compared to other modalities like X-ray radiography. Shortening scanning times is crucial in clinical settings, as it increases patient comfort, decreases examination costs and improves throughput. Recent advances in compressed sensing (CS) and deep learning allow accelerated MRI acquisition by reconstructing high-quality images from undersampled data. While reconstruction algorithms have received most of the focus, designing acquisition trajectories to optimize reconstruction quality remains an open question. This thesis explores two approaches to address this gap in the context of Cartesian MRI. First, we propose two algorithms, lazy LBCS and stochastic LBCS, that significantly improve upon G\"ozc\"u et al.'s greedy learning-based CS (LBCS) approach. These algorithms scale to large, clinically relevant scenarios like multi-coil 3D MR and dynamic MRI, previously inaccessible to LBCS. Additionally, we demonstrate that generative adversarial networks (GANs) can serve as a natural criterion for adaptive sampling by leveraging variance in the measurement domain to guide acquisition. Second, we delve into the underlying structures or assumptions that enable mask design algorithms to perform well in practice. Our experiments reveal that state-of-the-art deep reinforcement learning (RL) approaches, while capable of adaptation and long-horizon planning, offer only marginal improvements over stochastic LBCS, which is neither adaptive nor does long-term planning. Altogether, our findings suggest that stochastic LBCS and similar methods represent promising alternatives to deep RL. They shine in particular by their scalability and computational efficiency and could be key in the deployment of optimized acquisition trajectories in Cartesian MRI.

The modeling and forecasting of sea ice conditions in the Arctic region are important tasks for ship routing, offshore oil production, and environmental monitoring. We propose the adaptive surrogate modeling approach named LANE-SI (Lightweight Automated Neural Ensembling for Sea Ice) that uses ensemble of relatively simple deep learning models with different loss functions for forecasting of spatial distribution for sea ice concentration in the specified water area. Experimental studies confirm the quality of a long-term forecast based on a deep learning model fitted to the specific water area is comparable to resource-intensive physical modeling, and for some periods of the year, it is superior. We achieved a 20% improvement against the state-of-the-art physics-based forecast system SEAS5 for the Kara Sea.

Regularization is critical in solving the ill-posed geo-physical inversion problems. Explicit regularization is often used, but there are opportunities to explore the implicit regularization effect inherently from a Neural Network structure. Researchers in Computer Vision (CV) have discovered that the Convolutional Neural Network (CNN) architecture inherently enforces a regularization that is advantageous for addressing diverse CV inverse problems, including de-noising and in-painting. In this study, we examine the applicability of this implicit regularization to geophysical inversions. The CNN maps an arbitrary vector to the model space (e.g. log-conductivity on the simulation mesh). The predicted subsurface model is then fed into a forward numerical simulation process to generate corresponding predicted measurements. Subsequently, the objective function value is computed by comparing these predicted measurements with the observed field measurements. The backpropagation algorithm is employed to update the trainable parameters of the CNN during the inversion. Note that the CNN in our proposed method does not require training before the inversion, rather, the CNN weights are estimated in the inversion algorithm, hence this is a test-time learning (TTL) approach. The results demonstrate that the implicit regularization provided by the CNN can be useful in DC resistivity inversions. We also provide a detailed discussion of the potential sources of this implicit regularization and some practical guides for applying the proposed method to other geophysical scenarios. The proposed approach for reparameterizing the inverse problem can be adapted to other Tikhonov-style geophysical inversions.