相关论文: Ensemble Kalman Inversion method for an inverse pr…
In recent years, operator learning, particularly the DeepONet, has received much attention for efficiently learning complex mappings between input and output functions across diverse fields. However, in practical scenarios with limited and…
We present a novel sampling-based method for estimating probabilities of rare or failure events. Our approach is founded on the Ensemble Kalman filter (EnKF) for inverse problems. Therefore, we reformulate the rare event problem as an…
Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical…
We present a novel algorithm based on the ensemble Kalman filter to solve inverse problems involving multiscale elliptic partial differential equations. Our method is based on numerical homogenization and finite element discretization and…
The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…
Ensemble Kalman Sampler (EKS) is a method to find approximately $i.i.d.$ samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unknown. The continuous version of the algorithm is a set of…
Many parameter estimation problems arising in applications are best cast in the framework of Bayesian inversion. This allows not only for an estimate of the parameters, but also for the quantification of uncertainties in the estimates.…
Global ocean models exhibit biases in the mean state and variability, particularly at coarse resolution, where mesoscale eddies are unresolved. To address these biases, parameterization coefficients are typically tuned ad hoc. Here, we…
The Ensemble Kalman methodology in an inverse problems setting can be viewed as an iterative scheme, which is a weakly tamed discretization scheme for a certain stochastic differential equation (SDE). Assuming a suitable approximation…
Ensemble Kalman inversion is a parallelizable methodology for solving inverse or parameter estimation problems. Although it is based on ideas from Kalman filtering, it may be viewed as a derivative-free optimization method. In its most…
Different approaches to using data-driven methods for subgrid-scale closure modeling have emerged recently. Most of these approaches are data-hungry, and lack interpretability and out-of-distribution generalizability. Here, we use {online}…
Ensemble Kalman filtering (EnKF) is an efficient approach to addressing uncertainties in subsurface groundwater models. The EnKF sequentially integrates field data into simulation models to obtain a better characterization of the model's…
Reconstructing the structure of the soil using non-invasive techniques is a very relevant problem in many scientific fields, like geophysics and archaeology. This can be done, for instance, with the aid of Frequency Domain Electromagnetic…
Bayesian experimental design (BED) offers a principled framework for optimizing data acquisition by leveraging probabilistic inference. However, practical implementations of BED are often compromised by model discrepancy, i.e., the mismatch…
Ensemble smoother (ES) has been widely used in various research fields to reduce the uncertainty of the system-of-interest. However, the commonly-adopted ES method that employs the Kalman formula, that is, ES$_\text{(K)}$, does not perform…
Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an…
The unscented Kalman inversion (UKI) method presented in [1] is a general derivative-free approach for the inverse problem. UKI is particularly suitable for inverse problems where the forward model is given as a black box and may not be…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
Mathematical modeling and simulation of complex physical systems based on partial differential equations (PDEs) have been widely used in engineering and industrial applications. To enable reliable predictions, it is crucial yet challenging…
Approximate Bayesian computation (ABC) is the most popular approach to inferring parameters in the case where the data model is specified in the form of a simulator. It is not possible to directly implement standard Monte Carlo methods for…