Related papers: Reduced models with nonlinear approximations of la…

Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of…

Preferential diffusion plays a critical role in the evolution of lean premixed hydrogen flames, influencing flame surface corrugation and overall flame behavior. Simulating such flames with tabulated chemistry (TC) methods remains…

The accurate prediction of small scales in underresolved flows is still one of the main challenges in predictive simulations of complex configurations. Over the last few years, data-driven modeling has become popular in many fields as…

The use of model order reduction techniques in combination with ensemble-based methods for estimating the state of systems described by nonlinear partial differential equations has been of great interest in recent years in the data…

High-velocity streams of high-dimensional data pose significant "big data" analysis challenges across a range of applications and settings. Online learning and online convex programming play a significant role in the rapid recovery of…

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Predictive simulations are essential for applications ranging from weather forecasting to material design. The veracity of these simulations hinges on their capacity to capture the effective system dynamics. Massively parallel simulations…

Significant progress has been made on the model development for simulating turbulent reacting flows. As a consequence, we are currently in a position where key-physical aspects of fairly complex combustion processes are well understood at a…

Combustion stabilization and enhancement of the flammability limits are mandatory objectives to improve nowadays combustion chambers. At this purpose, the use of an electric field in the flame region provides a solution which is, at the…

The online optimization of gasoline blending benefits refinery economies. However, the nonlinear blending mechanism, the oil property fluctuations, and the blending model mismatch bring difficulties to the optimization. To solve the above…

Reduced order models, in particular the reduced basis method, rely on empirically built and problem dependent basis functions that are constructed during an off-line stage. In the on-line stage, the precomputed problem-dependent solution…

In this paper, we develop and analyze an adaptive multiscale approach for heterogeneous problems in perforated domains. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the…

Traditional model-based RL relies on hand-specified or learned models of transition dynamics of the environment. These methods are sample efficient and facilitate learning in the real world but fail to generalize to subtle variations in the…

The high sample complexity of reinforcement learning challenges its use in practice. A promising approach is to quickly adapt pre-trained policies to new environments. Existing methods for this policy adaptation problem typically rely on…

The estimation of model parameters with uncertainties from observed data is a ubiquitous inverse problem in science and engineering. In this paper, we suggest an inexpensive and easy to implement parameter estimation technique that uses a…

Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical…

The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…

We present a framework for analyzing the exact dynamics of a class of online learning algorithms in the high-dimensional scaling limit. Our results are applied to two concrete examples: online regularized linear regression and principal…

We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…