[
    {
        "id": "thesis:17725",
        "collection": "thesis",
        "collection_id": "17725",
        "cite_using_url": "https://resolver.caltech.edu/CaltechTHESIS:10202025-024638416",
        "primary_object_url": {
            "basename": "Caltech_Senior_Thesis.pdf",
            "content": "final",
            "filesize": 982758,
            "license": "cc_by_nc_sa",
            "mime_type": "application/pdf",
            "url": "/17725/1/Caltech_Senior_Thesis.pdf",
            "version": "v4.0.0"
        },
        "type": "thesis",
        "title": "Interacting Particle Systems for Sampling from Non-Gaussian Targets",
        "author": [
            {
                "family_name": "Teegavarapu",
                "given_name": "Ritvik S.",
                "orcid": "0000-0002-5970-9597",
                "clpid": "Teegavarapu-Ritvik-S"
            }
        ],
        "thesis_advisor": [
            {
                "family_name": "Hoffmann",
                "given_name": "Franca",
                "orcid": "0000-0002-1182-5521",
                "clpid": "Hoffmann-Franca"
            }
        ],
        "thesis_committee": [
            {
                "family_name": "Hoffmann",
                "given_name": "Franca",
                "orcid": "0000-0002-1182-5521",
                "clpid": "Hoffmann-Franca"
            },
            {
                "family_name": "Stuart",
                "given_name": "Andrew M.",
                "orcid": "0000-0001-9091-7266",
                "clpid": "Stuart-A-M"
            },
            {
                "family_name": "Hellmuth",
                "given_name": "Kathrin",
                "orcid": "0000-0002-5090-9218",
                "clpid": "Hellmuth-Kathrin-H"
            }
        ],
        "local_group": [
            {
                "literal": "div_eng"
            }
        ],
        "abstract": "<p>Sampling from a target distribution is a fundamental problem in applied mathematics, arising naturally in Bayesian inference and uncertainty quantification. Classical methods such as Markov Chain Monte Carlo can converge prohibitively slowly for complex, high-dimensional targets, and typically require access to gradient information that may be unavailable when the forward model is a black-box numerical solver. The Ensemble Kalman Sampler (EKS) addresses both difficulties, as it is a gradient-free interacting particle algorithm in which particles evolve under an empirical covariance-preconditioned force, making the dynamics affine invariant and well-adapted to the geometry of the target. As the number of particles tends to infinity, the empirical distribution of the EKS converges formally to a nonlinear PDE (the mean-field limit) which can be interpreted as a gradient flow in the Kalman-Wasserstein metric. However, rigorous justification of this mean-field limit has so far been confined to Gaussian or near-Gaussian targets, a restriction that precludes the majority of practical applications.</p>\r\n\r\n<p>This thesis develops a regularized variant of the EKS mean-field PDE, obtained by replacing the potential and entropy terms with mollified counterparts parameterized by a smoothing scale. This covariance-modulated blob flow inherits the gradient flow structure of EKS while admitting a rigorous analysis for general targets. We prove existence of weak solutions via a covariance-modulated JKO variational scheme, characterize the steady states and their bias, and prove convergence of the mollified solutions to the EKS mean-field PDE as we take the limit of the smoothing scale. Numerical experiments on benchmark targets confirm that the resulting particle algorithm is competitive with EKS in practice.</p>",
        "doi": "10.7907/jkfa-cc97",
        "publication_date": "2026",
        "thesis_type": "senior_major",
        "thesis_year": "2026"
    }
]