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Learning, Predicting and Control Diffusion via Optimal Transport
The stochastic diffusion equations ruling the dynamics of particles at the micro- and nano- scale are captured by energy-minimizing dynamics when observed macroscopically, i.e., at a population level. This framework encompasses, for instance, single cells perturbation responses to chemical, genetic or mechanical stimuli, gene expression and cell differentiation.
Recent advances in the theory of optimal transport and optimization in the Wasserstein space have created unprecedented opportunities to tackle these and other problems at scale. This active research area provides an excellent playground for exploring advanced mathematical concepts, deploying sophisticated learning and optimization algorithms, and solving open problems in biology, medicine, and various other fields.
The project can be both theoretical and applied, and can include topics on optimization, optimal transport, deep learning, and biology. The project can be tailored to the preferences and experiences of the student.
The stochastic diffusion equations ruling the dynamics of particles at the micro- and nano- scale are captured by energy-minimizing dynamics when observed macroscopically, i.e., at a population level. This framework encompasses, for instance, single cells perturbation responses to chemical, genetic or mechanical stimuli, gene expression and cell differentiation.
Recent advances in the theory of optimal transport and optimization in the Wasserstein space have created unprecedented opportunities to tackle these and other problems at scale. This active research area provides an excellent playground for exploring advanced mathematical concepts, deploying sophisticated learning and optimization algorithms, and solving open problems in biology, medicine, and various other fields.
The project can be both theoretical and applied, and can include topics on optimization, optimal transport, deep learning, and biology. The project can be tailored to the preferences and experiences of the student.
The stochastic diffusion equations ruling the dynamics of particles at the micro- and nano- scale are captured by energy-minimizing dynamics when observed macroscopically, i.e., at a population level. This framework encompasses, for instance, single cells perturbation responses to chemical, genetic or mechanical stimuli, gene expression and cell differentiation. Recent advances in the theory of optimal transport and optimization in the Wasserstein space have created unprecedented opportunities to tackle these and other problems at scale. This active research area provides an excellent playground for exploring advanced mathematical concepts, deploying sophisticated learning and optimization algorithms, and solving open problems in biology, medicine, and various other fields. The project can be both theoretical and applied, and can include topics on optimization, optimal transport, deep learning, and biology. The project can be tailored to the preferences and experiences of the student.