
Our team consists of engineers and scientists holding advanced degrees in a variety of disciplines. Broad range of areas we have worked on enables us to claim expertise in interdisciplinary problems that bridge mathematics, control, physical sciences and engineering. In particular, the interdisciplinary expertise of the team and sophisticated proprietary software enables us to solve a range of problems previously not accessible by computation. We specialize in providing accurate information from complex models even under substantial uncertainty in the data.
The particular technical areas of expertise in Aimdyn are:
Uncertainty is a measure of how large the deviations from a predicted behavior of a process can be. Decision makers often operate under large uncertainty in environmental or business conditions. For better results, complex simulation models are often used. But such models contain uncertainty themselves. For example, classically, single-trajectory computations of dynamical systems (e.g. oceanographic currents) are used for evaluation of engineered or natural system performance. However, in the context of uncertainties in modeling, parameter values and external conditions, simulation tools are needed where uncertainty in system components and architecture is simulated directly, providing a distribution of possible outcomes rather than a single one. Direct simulation in presence of P uncertain parameters, when each parameter range is discretized in N points yields PN simulations to be performed, thus leading to the exponential explosion of complexity or the so-called curse of dimensionality. We have developed methods for uncertainty analysis whose convergence does not depend on the dimension of the problem. The techniques are wrapper methods that do not change the simulation code itself, and can be applied even if the code itself is "black box" and only the inputs and outputs are accessible. This development provides Aimdyn with a unique capability to predict robust features of time-developing complex processes even if the underlying model is very uncertain. Based on this, Aimdyn developed decision making tools encoded in its GoSUM software. The tools that we developed stem from a large investment (about 4 mil/year for several years) of DARPA. The program brought together large industrial partners (United Technologies Corporation) with academia (UCSB, Caltech, Yale, Stanford) and small companies (Aimdyn, Plainsight) responsible for technology transition.
A complex system is any system featuring a large number of interacting components such as physical forces, social and engineered agents, whose aggregate activity is nonlinear (not derivable from the summations of the activity of individual components) and typically exhibits coherent emerging structures not predictable from individual component behavior.
Modern engineered systems all face a similar set of design challenges:
For example in design of fighter airplanes context, the number of control systems that provide optimal flight and fight conditions is growing and thus the number of scenarios where these systems have overlapping and possibly conflicting actions is growing as well. In ocean engineering, a number of different vessels and technologies might be deployed and coordinated from a command center. As the engineered system interacts with its environment, its control systems (including human and IT) provide for tactical and strategic decision-making functionality. However the situation when a single control system is operating is potentially quite different from the case in which multiple control systems are "on" simultaneously, and possibly have conflicting actions. Increasingly, due to the complexity vs. capacity issue, such issues are studied “in silico”. A computing model is designed, with a large number of parameters governing the dynamics. In the context of uncertainties in modeling, parameter values and external conditions, simulation tools are needed where uncertainty in system components and architecture is simulated directly, providing a distribution of possible outcomes rather than a single one. Direct simulation in presence of P uncertain parameters, when each parameter range is discretized in N points yields PN simulations to be performed, thus leading to the exponential explosion of complexity or the so-called curse of dimensionality. Since the whole system has a large number of degrees of freedom, a monolithic simulation of the system is often not feasible. The decomposition into components is necessary. But, such decomposition is not obvious due to complex, nonlinear interactions between various components. Aimdyn has developed proprietary software to address such questions and enable tactical and strategic decision-making. The core of Aimdyn’s technology are techniques that effectively reduce the enormous amount of available information to few key decision-making parameters.
The virtual reality concept of simulating and reconstructing system dynamics by the use of computer models is of great interest to the decision maker. The simulations consist usually in dividing the physical volume to be studied into a three-dimensional grid of tiny cells. The model then calculates changes in each cube by using fundamental equations of physics. For example, in the case of fluid flows, the underlying physics is within domain of fluid dynamics. The equations consist generally of a set of three-dimensional, time dependant, non-linear partial differential equations, referred to as the Navier-Stokes equations. These equations express conservation of mass, momentum, and energy. This process of solving the fundamental fluid dynamics with computers is commonly referred to as Computational Fluid Dynamics (CFD). The field model calculates the physical conditions of each cell, which results from changes in adjacent cells. If it is necessary to forecast effective strategic action, agent-based modeling tools are utilized in conjunction with physical equations. Agent-based modeling (ABM) consists of a new approach simulating the behavior of a complex system in which agents interact with each other and with their environment using simple local rules. This approach has already proven successful in predicting traffic flow in metropolitan areas, the spread of infectious diseases, and the behavior of economic systems. Aimdyn has expertise in a variety of agent-based modeling techniques. These techniques can be coupled with the physical modeling methods described above to represent the full, physical-social system and result of a variety of proposed control actions on it. The resulting system is simulated in time and state variables are predicted. However, the amount of information in such variables might be too large ("gigabytes of data") for the decision maker to process in a short amount of time available to make the decision. This is why Aimdyn develops forecasting, sensitivity analysis and uncertainty analysis tools. These tools extract only the most pertinent, robust information from the state variables. Based on this, Aimdyn scientists are able to demonstrate how various tactical and strategic approaches are likely to affect process development under varying environmental conditions, parameters and despite uncertainty present in underlying models.