The Shaping of Better Decisions: Using Topology to Help Decision-Makers Navigate Complex Systems

Have you ever tried to understand a complex system by looking at a mountain of data and wondered: "What am I actually seeing here?" This challenge hit home for me while studying how different sectors of our society—energy, water, climate, economy—all interact with each other. To understand these systems, researchers use what we call "exploratory modeling"—imagine testing a car's performance not just under one or two conditions, but under every possible combination of weather, road type, speed, and driver behavior. Each test creates a data point, and when you're testing thousands of possibilities, you end up with a vast cloud of these points, each representing a possible future scenario.

Let me explain why this matters. When policymakers need to make decisions about climate adaptation, energy transitions, or resource management, they can't just guess what might happen—they need to understand how their decisions might play out across countless possible futures. Traditional mathematical approaches fall short here for two reasons: first, these systems are too complex to solve with direct equations (imagine trying to write a single equation that captures all the ways the economy affects the climate, and vice versa). Second, while we can sometimes understand simpler systems by visualizing their behavior in graphs, this approach breaks down when dealing with hundreds of interacting factors—it's like trying to draw a map of a hundred-dimensional city.

This is where Project Envision comes in. We're turning to topology—a branch of mathematics that studies the fundamental shapes and structures of spaces—to help us understand these complex systems. The beauty of topology lies in its ability to find patterns that persist regardless of the exact details. Think about how topology tells us that a coffee cup and a donut are fundamentally similar because they both have one hole—it doesn't care about the exact shape, only the essential structure. Similarly, by applying topological data analysis (TDA) combined with artificial intelligence, we're developing a system that can identify the essential patterns in our massive clouds of data points, patterns that might tell us which decisions are consistently better across many possible futures.

The potential impact of this work excites me. While we're still in the early stages, we envision a future where policymakers can better understand the consequences of their decisions across multiple sectors. Instead of being overwhelmed by complexity, they could see clear pathways through it. For instance, we might be able to identify previously hidden connections between energy policy decisions and water resource impacts, or understand how economic policies might affect climate resilience across different regions.

What makes this approach unique is its ability to work with uncertainty rather than trying to eliminate it. Traditional methods often struggle when dealing with complex systems where we can't predict everything perfectly. Our topological approach embraces this uncertainty while still finding meaningful patterns within it.

Looking ahead, I believe this project could change how we approach decision-making for complex societal challenges. As we face increasingly interconnected problems like climate change, energy transitions, and resource management, we need better tools to understand how our decisions ripple across different sectors of society.

As a researcher, watching this project evolve from a mathematical concept to a potentially practical tool has been fascinating. While there's still much work to be done—testing different topological methods, refining our AI approaches, and validating results—each step brings us closer to helping decision-makers navigate the complexity of our interconnected world more effectively.

The journey from abstract mathematics to real-world impact isn't always straightforward, but when I think about how this work could help communities make better decisions about their future, it makes all the theoretical challenges worth tackling. After all, sometimes the most practical solutions come from the most abstract places.