2026 | Math to Power Industry

Awesense

Tue, 24 Mar 2026 00:00:00 +0000

At Awesense, we’ve been building a platform for power grid digital twins with the goal of allowing easy access to and use of electrical grid data in order to build a myriad of applications and use cases for the decarbonized grid of the future, which will need to include more and more distributed energy resources (DERs) such as rooftop solar, batteries as well as electric vehicles (EVs) and still operate safely and efficiently.

Awesense has built a sandbox environment populated with synthetic but realistic data and exposing APIs on top of which such applications can be built. As such, what we are looking for is to create a collection of prototype applications demonstrating the power of the platform.

The current challenge involves building computational techniques for automatically detecting the presence of behind-the-meter electric vehicles and disaggregating their consumption from the overall household (meter) consumption.

Background

Energy disaggregation, also known as appliance disaggregation is a technique which is used to analyze and break down the energy consumption in a building or household into individual appliance-level energy usages. The goal is to identify and monitor the energy consumption of specific “appliances” without the need for additional metering or sensors on each device.

The process of energy disaggregation involves analyzing the overall power signal from a building or household and applying advanced algorithms and machine learning techniques to separate and attribute energy consumption to specific sources. One of these sources can be electric vehicles (EVs), particularly ones plugged-in directly into regular outlets. These are the focus of the proposed project.

The ability to perform energy disaggregation analytics holds significant importance for utilities and electricity distribution. By gaining granular insights into customers’ energy usage at a more granular level, utilities can develop targeted demand response programs, optimize load distribution, and enhance grid management. Energy disaggregation analytics enables utilities to identify peak demand periods, forecast load patterns, and make informed decisions regarding infrastructure investments.

Details

Electrical distribution grids are composed of grid elements of various types (e.g. power lines, transformers, switches, meters, SCADA devices, etc.) connected to each other in a network (graph) structure. A feeder is a set of distribution lines (often operating at medium voltage) that collectively transport power from a substation to a multitude of downstream loads. Certain grid elements like meters, SCADA devices, fixed or movable IoT sensors, and Distributed Energy Resources (DERs) produce time series data such as voltage, current, power, energy, battery state of charge, and other measurements.

In this project, the students will need to use the Awesense SQL or REST APIs to retrieve the necessary time series and grid structure information to determine (and visualize) which households (meters) likely have an electric vehicle, at what times is it plugged in and how much energy does it draw.

Additional information about the EV disaggregation use case can be found here.

Skillset

This work involves coding some analyses and visualizations on top of the data and APIs described above and devising an algorithm for the redistribution of load to optimize overall capacity. It would require good data wrangling, statistics and data visualization skills to design and then implement the best way to transform, aggregate and visualize the data, and good mathematical/algorithmic skills for the optimization piece. The data access APIs are in SQL form, so SQL querying skills would also be desirable. Alternatively, REST APIs can be made available. Beyond that, the tools and programming languages used to create the analyses, visualizations and algorithms would be up to the students. Typical ones we have used include BI tools like Power BI or Tableau and notebooking applications like Jupyter or Zeppelin combined with programming languages like Python or R.

Tool Access and Support

If the participants don’t have any electrical background, Awesense will teach enough of it to allow handling the given use case.

In addition to the previously mentioned SQL and REST APIs, the Awesense platform also comes with a web-based application (graphical user interface front-end) called TGI (True Grid Intelligence) that serves as a companion visual explorer for the data stored in the platform. The snapshot below shows a portion of the grid available in the synthetic dataset. An EV Charger is selected (map blue marker and highlighted row in the table) and its properties are shown in the left sidebar, along with an electrical flow time series chart. The SQL & REST APIs include functionality for retrieving all this information programmatically.

For the duration of the project, upon agreeing to a standard end-user licensing agreement, participants in this PIMS project will be given access to the sandbox environment, including TGI, the programmatic SQL and REST APIs and associated documentation, as well as access to a GitHub repository with sample SQL, REST and python code snippets in Jupyter notebooks, showcasing how to use the APIs.

A successful project will consist of an algorithm and a set of visuals answering the questions posed above for the sandbox dataset, accompanied by any BI tool files or notebook code used to produce them; Awesense permits and encourages the public sharing of these artifacts, as long as credit for the dataset and APIs is given to Awesense (e.g. by including a “Powered by Awesense” phrase and an Awesense website link; publishing the raw data retrieved from the sandbox is not permitted.

Important note : project participants will be given individual access credentials, and they should not share with anyone else (including not among themselves) nor cache/save them in publicly posted files.

Environment and Climate Change Canada

Tue, 24 Mar 2026 00:00:00 +0000

Introduction

The training of a neural network is the most cost-consuming part of scientific machine learning. The optimizers are algorithms used to adjust model parameters to minimize the loss function. The optimizers determine the efficiency of the training approach and the quality of the resulting model. No one single optimizer is fit for all problems.

The PARADIS model is a data-driven model developed by Environment and Climate Change Canada (ECCC) for medium-range global weather forecasting. The goal of this project is to compare various optimization protocols during the training of the PARADIS model.

Data set

Shallow Water Equations

(SWE) Due to the size of the ERA-5 global weather dataset, it is more suitable to use the data generated by SWE for this project.

Optimizers for comparison

AdamW
SGD
Muon
etc.

Metric of comparison

Efficiency: the rate of convergence
Quality: The loss of the optimized point, the spectral of the optimized point.

N.B. Students are required to have access to GPU for training.

Hummingbird Bioscience

Tue, 24 Mar 2026 00:00:00 +0000

Recently, the quest for mathematical superintelligence has become a focal point in artificial intelligence. For example, Robinhood’s spinoff Harmonic has achieved a valuation exceeding $1 billion with its Aristotle tool. A key reason for this excitement is that mathematical reasoning is fundamentally different from other forms of reasoning: it is, by nature, airtight. It was believed that AI systems would struggle with this domain. However, recent advances suggest otherwise.

Modern systems are increasingly capable of translating between informal mathematical language (as written in papers) and formal representations suitable for proof assistants such as Lean, Rocq, or Agda. One striking example includes the recent overturning of a long-standing result in an extended quantum field theory, previously cited hundreds of times over more than a decade. However, these systems are demonstrating strong performance primarily on carefully selected, benchmark-style problems or carefully chosen problems. Their behavior outside of these settings remains poorly understood.

In particular, while they can often verify closed-form results in isolation, they often struggle to correctly represent and validate the dependencies those results rely on. This creates a critical reliability gap: outputs may appear correct locally while being globally inconsistent.

As an industry partner developing AI systems for mathematical reasoning, we are directly interested in understanding the limits of these auto-formalization tools. Without a systematic understanding of their failure modes, deploying such systems introduces substantial risk. This is made worse as organizations begin making significant financial and strategic decisions based on their outputs.

Project Objective

This project will investigate the robustness of auto-formalization systems by identifying and characterizing their failure modes. Teams will:

Explore how current systems translate informal mathematics into formal representations
Identify classes of problems where these systems perform well and where they fail
Develop strategies—such as adversarial search or evolutionary (genetic) methods—to generate mathematical inputs that induce failure
Analyze and categorize failure modes, with particular attention to dependency structure and logical consistency

Deliverables

Challenging mathematical statements on which tools struggle or fail
A taxonomy of observed failure modes
Quantitative or qualitative metrics for evaluating system robustness
Bonus: Recommendations for improving reliability in auto-formalization systems

Why This Matters

These systems can already produce convincing formal outputs. However, without understanding when and how they fail—particularly in handling dependencies—their use in research, verification, and high-stakes applications remains fundamentally limited. This project aims to make this gap more visible.

Teams may consider approaches such as:

Restricting to a specific domain (e.g., algebraic identities, inequalities, combinatorics, measure theory, symplectic geometry, etc.)
Designing perturbations of known theorems to test robustness
Modeling the search space of candidate statements
Using adversarial or evolutionary methods to discover failure cases

Further, we will assist teams in getting bootstrapped to experimentation with both closed and open-source LLMs and auto-formalization tools, and help set up tooling for advanced search methods such as adversarial or genetic approaches.

One Child Every Child

Tue, 24 Mar 2026 00:00:00 +0000

This project examines how re-identification risk varies within datasets, particularly for individuals with unique or complex diagnostic profiles, and identifies factors beyond average sample-level risk that contribute to vulnerability. It aims to assess how data type, dataset structure, and existing safeguards influence re-identification risk, with a focus on informing responsible data sharing practices for research involving children with complex diagnoses.

Introduction

Re-identification risk is disproportionately shouldered by individuals with unique data profiles (i.e., outliers), including children with complex diagnostic profiles. There is also limited literature on the factors that might influence re-identification risk beyond the risk to the whole sample on average.

With the increase in requirements for data sharing, it is important to understand re-identification risk within a sample, but also the re-identification risk of individuals who are unique. Considerations should be made that there are some risks that are not within the control of researchers (e.g., knowing whether someone is in a study or not; a family might willingly share this information). Thus, extra consideration should be made for those things that can be controlled by the research team while appreciating the importance of data sharing and utilization of research data.

GOAL

The goal of this study is to determine factors contributing to re-identification risk in large datasets and their impact on children with complex diagnostic profiles.

Aim 1

What kind of data is at risk for re-identification and what recommendations have been made within the literature?

With the utilization of publicly available data to train AI models, it is becoming increasingly important for researchers to clearly communicate to research participants how their data will be used and the risk associated with data sharing. The first aim of this study will look at the existing literature and assess the recommendations that have been made to limit re-identification risk in research data. This aim will also address the existing literature that has evaluated re-identification risk in specific types of data and the differences in recommendations based on data type (i.e., MRI, genetic, behavioural, etc.).

Aim 2

How does the shape of the data influence re-identification risk within a randomly generated sample and is this comparable to a sample generated based on known variable relationships?

Aim 2.1

What factors contribute to greater re-identification risk in a sample of randomly generated data Assuming that re-identification risk is influenced by several factors including

the number of possible combinations of variables (# of possible unique ‘profiles’)
the size of the sample
the variability of each of the variables (i.e., how likely are there to be outliers, especially ’extreme’ outliers), and
the number of shared variables which could be considered identifiable.

The shape of the dataset could influence re-identification risk and by understanding the relationship between the shape of the dataset and re-identification risk we can determine the risk level of data sharing. Particularly for individuals who might have ‘unique’ data profiles which might be more likely to be re-identified.

Aim 2.2

Does a sample that is based on known variable relationships (co-occurrence between neurodevelopmental disorders) behave the same way as a fully synthetic dataset?

One use case where re-identification risk is of particular concern in within populations of children with unique diagnostic profiles (unique combinations of diagnoses). Given the high rate of co-occurrence in these disorders, it is common for a child to present with multiple diagnoses. Determine the co-occurrence rates for several neurodevelopmental disorders (Autism, ADHD, OCD, CD, ODD, etc.)

Type One Energy

Tue, 24 Mar 2026 00:00:00 +0000

The purpose of this project is to identify, through numerical optimization, fusion reactor shapes which maximize the average pressure of the fusion fuel.

About Type One Energy

At Type One Energy Group, Inc., we are developing optimized stellarator designs to provide sustainable, affordable fusion power to the world. We apply proven advanced manufacturing methods, modern computational physics and high-field superconducting magnets to pursue the lowest-risk, shortest-schedule path to a fusion power plant over the coming decade.

The Problem

The goal of the project is to determine, via the application of local, global, and machine-learning based numerical optimization algorithms, the cross-sectional shapes of fusion reactors which maximize the average pressure of the fusion fuel. Since the average pressure is computed from the solution of a partial differential equation (PDE) describing force balance for the fusion fuel inside the reactor, this is a PDE constrained shape optimization problem.

The Type One Energy mentor will provide the complete description of the PDE to be solved and of the toroidal geometry we will work with. They will also provide Python examples of numerical solvers for the PDE of interest. The participants will therefore focus their efforts on the development of optimization algorithms for this shape optimization problem.

Skillset

The project requires a good command of standard numpy tools and programming practices in Python. It also requires a good understanding of elementary partial differential equations (e.g. the first 4 chapters of Evans’ PDE textbook) and a good understanding of elementary numerical analysis / scientific computing. No prior knowledge of fusion or plasma physics is required. We will be happy to teach participants as much about fusion and plasma physics as they would like to learn!

If we make good progress on this project, it may become valuable to become familiar with Python-based automated frameworks for solving partial differential equations, such as Firedrake or FEniCS.

IOTO

Tue, 24 Mar 2026 00:00:00 +0000

Overview

We have controlled vocabularies and topic structures that are used to index and understand large bodies of text. We want to better understand how text is clustered around known structured topics so that unknown topics can be identified in texts and added to our controlled vocabularies and topic structures.

Background

Goverlytics^® seeks to produce low-dimensional representations of legislative activity to: 1) make politics accessible to a broader public; and to 2) increase focus on policy goals. The model for Goverlytics^® is sports analytics, which has transformed the way in which sports are understood and consumed. Goverlytics^® analyzes data generated during legislative sessions: attendance, documents, transcripts, vote tallies, audio and video recordings.

Analytics in sports first began with measurement of what could be easily measured – goals (of course!), strokes, hits, etc. By distilling all that goes on during the activity into a few dimensions that allow for quantification and comparison, analytics helps to explain and so increase comprehension and engagement. Increasingly complex measurements are being engineered from ever larger datasets to enhance predictions and decision-making. Both short-term outcomes and strategies that may be decided in game, and for long-term considerations such as player health are at stake.

Challenge

In some cases, Goverlytics^® has to start creating statistics for legislative sessions from simple audio tracks. Audio is transcribed into words of a language. Then the language words (and concatenations of them) are binned into topic discourse, by means language models and topic classifications. Finally, topic classifications are used to index parts of the legislative activity that are likely to be interesting for a broader public. This process is akin to the distillation of a sporting match into a highlights reel or abbreviated match summary e.g. What topics were discussed the most? Who talked about those topics? Were there any significant new topics, or was voting and discussion about previously known topics? Were there significant outliers? Smash hits?

Because legislative sessions can go on for hours with very little information of predictive or decision-making value, it can be costly to process raw data to reach insight. The challenge is to find shorter paths to interesting bits of discourse. Can methods from signal analysis or related mathematical fields be used to more efficiently signpost insight into legislative data? Unsupervised learning techniques may provide some guidance. However, a successful solution will reveal what in the legislative activity is deserving of attention from a policy point of view, ether by connecting with a known policy ontology (such as comparative agendas codebook, or by surfacing issues that should be connected to a known ontology.

Data

At a minimum, APIs covering topic data for various legislative leagues (Canada, BC, Alberta, etc.) will be made available to the M2PI team. These APIs reliably serve data concerning legislative ‘players’ and their topic-related interventions over a number of legislative sessions. Corresponding audio will also be supplied.

Further datasets concerning elections, voting, and financial data may be made available – depending time available, which legislative leagues the M2PI team elects to study, and how they choose to analyse.

Finance data are available from OECD, Statistics Canada, and legislative ’leagues’ themselves.
Topics are standardized along Comparative Agendas Project (CAP) lines
Charts of accounts for finance overlap topic categories, but do not correspond exactly.
Voting data for bills and motions may be available for certain legislatures.
Audio files are available for whatever legislative level is chosen for study by the M2PI team.

Quantum Advantage Partners

Tue, 24 Mar 2026 00:00:00 +0000

Overview

In real organizations, each role (CEO, CFO, VP Sales…) sees different information and applies different decision criteria — yet every multi-agent simulation framework today gives all agents the same shared context. We want to mathematically test whether modeling information compartmentalization and role-specific decision processes produces measurably better collective outcomes than the standard shared-context approach.

Problem Statement

Multi-agent simulation frameworks (CrewAI, TinyTroupe, Concordia) model organizations by assigning role labels to agents that all share the same information. This ignores two fundamental features of real organizations:

information is compartmentalized — a CFO doesn’t know everything the VP Sales knows, and vice versa;
each role processes information differently — applying distinct criteria, thresholds, and filters when making decisions.

We propose a rule-based (no LLM, no API costs) agent-based simulation of a simplified company with 5-7 roles operating in a stochastic market environment.

Three configurations are tested against identical market scenarios:

Baseline: shared context, simple role labels only.
Decision process modeling: shared context, but each role applies role-specific decision functions (different weights, thresholds, filters).
Full compartmentalization: role-specific information subsets AND role-specific decision functions. Each configuration is run M times across N simulated quarters using Monte Carlo methods.

Primary metric: cumulative simulated revenue.

Secondary metrics:

decision speed (cycles to consensus)
decision reversal rate (coherence proxy), and information request patterns between agents.

The mathematical work involves:

formalizing agent decision functions and information partition matrices,
designing the stochastic market environment, specifying the experimental design (factorial or fractional factorial),
running simulations in Python, and performing statistical hypothesis testing to compare outcome distributions across configurations A/B/C.

A sensitivity analysis identifies which compartmentalization parameters have the largest effect on outcomes, including boundary conditions where compartmentalization may hurt rather than help performance.

Expected background

probability
stochastic processes
statistical inference
Python (NumPy/SciPy).

Game theory or mechanism design is a plus but not required. The industry mentor (Mehdi Bozzo-Rey, QAP) will provide will provide the initial conceptual model of role-specific decision processes, informed by applied work in deeptech commercialization advisory.

The team will collaboratively formalize this model into mathematical specifications during week 1, then implement and test it in weeks 2-3.

University of Victoria

Tue, 24 Mar 2026 00:00:00 +0000

Overview

The goal of this project is to develop an interface between quantum and classical (binary) computing systems for climate modeling.

Climate models are large, complex computer programs made up of multiple components that represent different parts of the Earth system, such as the atmosphere, oceans, cryosphere, and vegetation. Each component is typically developed as a separate code, and many of these are further divided into sub-modules.

For example, atmospheric models usually include a dynamics module—often called the dynamical core—and one or more physics modules. The dynamical core is based on systematic discretization methods (such as finite differences, finite volumes, or spectral methods) to solve the equations of motion. In contrast, the physics modules represent processes that are not explicitly resolved by the dynamical core. These processes occur at spatial or temporal scales smaller than the model’s grid resolution and include phenomena such as radiation, phase changes of water and associated latent heat transfer, turbulence, and convection.

Because resolving these small-scale processes directly is computationally expensive, they are typically approximated using heuristic models based on ad hoc closure assumptions.

Although quantum computing is advancing rapidly, it is not yet practical to implement all components of climate models on quantum systems. Moreover, existing classical codes for dynamical cores are well established and highly reliable. However, if a quantum algorithm can be developed for specific sub-grid processes that is both efficient and accurate, it could be integrated with a classical dynamical core to create a hybrid quantum–classical modeling framework.

As a proof of concept, this project proposes to couple a simple convection model with a toy climate model developed by Khouider et al. (2010). The convection model, known as the Stochastic Multicloud Model (SMCM), is a Markov model that describes the area fractions of three cloud types.

In Khouider et al. (2010), the SMCM is coupled with a set of ordinary differential equations (ODEs) that describe the vertical profiles of temperature and moisture, assuming horizontal homogeneity (i.e., no spatial derivatives). More recently, Ueno and Miura (2025) developed a quantum implementation of the SMCM component alone.

This project aims to integrate the quantum SMCM code of Ueno and Miura (2025) with the ODE-based system used in Khouider et al. (2010), which serves as a simplified dynamical core. This integration will act as a demonstration of a hybrid quantum–classical climate modeling approach.

As a possible extension, the quantum SMCM code could also be applied to machine learning tasks. For example, it could be used to generate sample paths for a synthetic likelihood algorithm to calibrate the SMCM using radar data (Sevilla and Khouider, unpublished work).

References

Kazumasa Ueno, Hiroaki Miura, Quantum Algorithm for a Stochastic Multicloud Model, SOLA, 2025, Vol. 21, pp. 43-50, Publication Date 2025/01/22, [Early Release] Publication Date 2024/12/11, Online ISSN 1349-6476, https://doi.org/10.2151/sola.2025-006.
Khouider, B., J. Biello, and A. J. Majda, 2010: A stochastic multicloud model for tropical convection. Commun. Math. Sci., 8, 187–216.