Search for: All records

Neurovascular coupling (NVC) is the ability to locally adjust vascular resistance as a function of neuronal activity. Recent experiments have illustrated that NVC is partially independent of metabolic signals. In addition Nitric Oxide (NO) has been shown in some instances to provide an important mechanism in altering vascular resistance. An extension to the original model of NVC [1] has been developed to include the activation of both somato-sensory neurons and GABAergic interneurons and to investigate the role of NO and the delicate balance of GABA and neuronal peptide enzymes (NPY) pathways. The numerical model is compared to murine experimental data that provides time-dependent profiles of oxy, de-oxy and total-haemoglobin. The results indicate a delicate balance that exists between GABA and NPY when n-NOS interneurons are activated mediated by NO. Whereas somato-sensory neurons (producing potassium into the extracellular space) do not seem to be effected by the inhibition of NO. Further work will need to be done to investigate the role of NO when stimulation periods are increased substantiallyfrom the short pulses of 2 seconds as used in the above experiments. 

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models.A well-known Achilles' heel of this approach is its computational cost, which often renders it unfeasible in practice. An appealing alternative is to instead analyze the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy. Should a surrogate be simple enough to be amenable to the analytical calculations of its Sobol' indices, the cost of GSA is essentially reduced to the construction of the surrogate.We propose a new class of sparse-weight extreme learning machines (ELMs), which, when considered as surrogates in the context of GSA, admit analytical formulas for their Sobol' indices and, unlike the standard ELMs, yield accurate approximations of these indices. The effectiveness of this approach is illustrated through both traditional benchmarks in the field and on a chemical reaction network. 

We present a computational framework for dimension reduction and surrogate modeling to accelerate uncertainty quantification in computationally intensive models with high-dimensional inputs and function-valued outputs. Our driving application is multiphase flow in saturated-unsaturated porous media in the context of radioactive waste storage. For fast input dimension reduction, we utilize an approximate global sensitivity measure, for function-valued outputs, motivated by ideas from the active subspace methods. The proposed approach does not require expensive gradient computations. We generate an efficient surrogate model by combining a truncated Karhunen-Loeve (KL) expansion of the output with polynomial chaos expansions, for the output KL modes, constructed in the reduced parameter space. We demonstrate the effectiveness of the proposed surrogate modeling approach with a comprehensive set of numerical experiments, where we consider a number of function-valued (temporally or spatially distributed) QoIs.