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The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from…
Complex dissipative systems appear across science and engineering, from polymers and active matter to learning algorithms. These systems operate far from equilibrium, where energy dissipation and time irreversibility govern their behavior…
Deep learning method has attracted tremendous attention to handle fluid dynamics in recent years. However, the deep learning method requires much data to guarantee the generalization ability and the data of fluid dynamics are deficient.…
While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from {\em small} data. In…
A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
We present a novel interpretable machine learning model to accurately predict complex rippling deformations of Multi-Walled Carbon Nanotubes(MWCNTs) made of millions of atoms. Atomistic-physics-based models are accurate but computationally…
The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…
The Bayesian update step poses significant computational challenges in high-dimensional nonlinear estimation. While log-homotopy particle flow filters offer an alternative to stochastic sampling, existing formulations usually yield stiff…
Kinetic approaches are generally accurate in dealing with microscale plasma physics problems but are computationally expensive for large-scale or multiscale systems. One of the long-standing problems in plasma physics is the integration of…
We consider the out-of-equilibrium dynamics of an interacting integrable system in the presence of an external dephasing noise. In the limit of large spatial correlation of the noise, we develop an exact description of the dynamics of the…
An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
The goal of generative models is to learn the intricate relations between the data to create new simulated data, but current approaches fail in very high dimensions. When the true data generating process is based on physical processes these…
Physics-based numerical models have been the bedrock of atmospheric sciences for decades, offering robust solutions but often at the cost of significant computational resources. Deep learning (DL) models have emerged as powerful tools in…
We present a deep learning-based object detection and object tracking algorithm to study droplet motion in dense microfluidic emulsions. The deep learning procedure is shown to correctly predict the droplets' shape and track their motion at…
The dynamics of flexible filaments entrained in flow, important for understanding many biological and industrial processes, are computationally expensive to model with full-physics simulations. This work describes a data-driven technique to…
We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying…
For decades, people have been seeking for fishlike flapping motions that can realize underwater propulsion with low energy cost. Complexity of the nonstationary flow field around the flapping body makes this problem very difficult. In…
We present a hydro-geomechanical model for subsurface methane hydrate systems. Our model considers kinetic hydrate phase change and non-isothermal, multi-phase, multi-component flow in elastically deforming soils. The model accounts for the…