Gauging the resilience of complex networks
Single equation proposed to predict strength of ecosystems, power grids, internet, and other systems

Date:
January 10, 2022
Source:
Rensselaer Polytechnic Institute
Summary:
Whether a transformer catches fire in a power grid, a species
disappears from an ecosystem, or water floods a city street, many
systems can absorb a certain amount of disruption. But how badly
does a single failure weaken the network? And how much damage can
it take before it tips into collapse?


FULL STORY ========================================================================== Whether a transformer catches fire in a power grid, a species disappears
from an ecosystem, or water floods a city street, many systems can
absorb a certain amount of disruption. But how badly does a single
failure weaken the network? And how much damage can it take before it
tips into collapse? Network scientist Jianxi Gao is building tools that
can answer those questions, regardless of the nature of the system.


========================================================================== "After a certain point, damage to a system is so great that it causes catastrophic failure. But the events leading to a loss of resilience in a system are rarely predictable and often irreversible. That makes it hard
to prevent a collapse," said Dr. Gao, an assistant professor of computer science at Rensselaer Polytechnic Institute, who was awarded a National
Science Foundation CAREER award to tackle the problem. "The mathematical
tools we are building will make it possible to evaluate the resilience
of any system. And with that, we can predict and prevent failure."
Imagine the effects of climate change on an ecosystem, Dr. Gao said. A
species that can't adapt will dwindle to extinction, perhaps driving a
cascade of other species, which eat the first, to the brink of extinction
also. As the climate changes, and more species are stressed, Dr. Gao
wants the ability to predict the impact of those dwindling populations
on the rest of the ecosystem.

Predicting resilience starts by mapping the system as a network, a graph
in which the players (an animal, neuron, power station) are connected by
the relationships between them, and how that relationship affects each of
the players and the network overall. In one visualization of a network,
each of the players is a dot, a node, connected to other players by
links that represent the relationship between them -- think who eats
whom in a forest and how that impacts the overall population of each
species, or how information moving across a social media site influences opinions. Over time, the system changes, with some nodes appearing or disappearing, links growing stronger or weaker or changing relationship
to one another as the system as a whole responds to that change.

Mathematically, a changing network can be described by a series of
coupled nonlinear equations. And while equations have been developed
to map networks in many fields, predicting the resiliency of complex
networks or systems with missing information overwhelms the existing
ability of even the most powerful supercomputers.

"We're very limited in what we can do with the existing methods. Even
if the network is not very large, we may be able to use the computer
to solve the coupled equations, but we cannot simulate many different
failure scenarios," Dr. Gao said.

Dr. Gao debuted a preliminary solution to the problem in a 2016 paper
published in Nature. In that paper, he and his colleagues declared that existing analytical tools are insufficient because they were designed for smaller models with few interacting components, as opposed to the vast
networks we want to understand. The authors proposed a new set of tools, designed for complex networks, able to first identify the natural state
and control parameters of the network, and then collapse the behavior
of different networks into a single, solvable, universal function.

The tools presented in the Nature paper worked with strict assumptions
on a network where all information is known -- all nodes, all links, and
the interactions between those nodes and links. In the new work, Dr. Gao
wants to extend the single universal equation to networks where some
of the information is missing. The tools he is developing will estimate
missing information - - missing nodes and links, and the relationships
between them -- based on what is already known. The approach reduces
accuracy somewhat, but enables a far greater reward than what is lost,
Dr. Gao said.

"For a network of millions or even billions of nodes, I will be able
to use just one equation to estimate the macroscopic behavior of the
network. Of course, I will lose some information, some accuracy,
but I capture the most important dynamics or properties of the
whole system," Dr. Gao said. "Right now, people cannot do that. They
cannot test the system, find where it gives way, and better still,
improve it so that it will not fail." "The ability to analyze and
predict weaknesses across a variety of network types gives us a vast
amount of power to safeguard vulnerable networks and ecosystems
before they fail," said Curt Breneman, dean of the Rensselaer
School of Science. "This is the kind of work that changes the
game, and this CAREER award is a recognition of that potential. We
congratulate Jianxi and expect great things from his research." ========================================================================== Story Source: Materials provided by
Rensselaer_Polytechnic_Institute. Original written by Mary
L. Martialay. Note: Content may be edited for style and length.


==========================================================================


Link to news story: https://www.sciencedaily.com/releases/2022/01/220110132755.htm
--- up 5 weeks, 2 days, 7 hours, 13 minutes
* Origin: -=> Castle Rock BBS <=- Now Husky HPT Powered! (1:317/3)